a. books and theses€¦ · references a. books and theses [abr97] p. abry, ondelettes et...

References

A Books and Theses

[Abr97] P Abry Ondelettes et turbulences mdash Multireacutesolutions algorithmes de deacutecompositioninvariance drsquoeacutechelle et signaux de pression (Diderot Paris 1997)

[Adl95] SL Adler Quaternionic Quantum Mechanics and Quantum Fields (Oxford Univer-sity Press New York 1995)

[Akh65] NI Akhiezer The Classical Moment Problem and Some Related Questions inAnalysis (Oliver and Boyd Edinburgh and London 1965)

[Ala94] A Alaux Lrsquoimage par reacutesonance magneacutetique (Sauramps Meacutedical Montpellier 1994)[Ald96] A Aldroubi M Unser (eds) Wavelets in Medicine and Biology (CRC Press Boca

Raton 1996)[Ali07] ST Ali M Engliš Berezin-Toeplitz quantization over matrix domains in Contribu-

tions in Mathematical Physics ndash A tribute to Geacuterard Emch Ed by ST Ali KB Sinha(Hindustan Book Agency New Delhi India 2007)

[And13] TD Andrews R Balan JJ Benedetto W Czaja KA Okoudjou (eds) Excursionsin Harmonic Analysis vol 1 2 (Birkhaumluser Boston 2013)

[Ant04] J-P Antoine R Murenzi P Vandergheynst ST Ali Two-Dimensional Wavelets andtheir Relatives (Cambridge University Press Cambridge (UK) 2004)

[Ant09] J-P Antoine C Trapani Partial Inner Product Spaces mdash Theory and ApplicationsLecture Notes in Mathematics vol 1986 (Springer Berlin Heidelberg 2009)

[Arn95] A Arneacuteodo F Argoul E Bacry J Elezgaray JF Muzy Ondelettes multifractaleset turbulences ndash De lrsquoADN aux croissances cristallines (Diderot Paris 1995)

[Asc72] E Ascher Extensions et cohomologie de groupes Lecture Notes Enseignement dutroisiegraveme cycle de la physique en Suisse Romande (CICP) (1972)

[Bar77] AO Barut R Raczka Theory of Group Representations and Applications (PWNWarszawa 1977)

[Bec06] K Becker M Becker JH Schwarz String Theory and M-Theory A ModernIntroduction (Cambridge University Press Cambridge 2006)

[Ben01] JJ Benedetto PJSG Ferreira Modern Sampling Theory Mathematics and Appli-cations (Birkhaumluser Boston Basel Berlin 2001)

[Ben04] JJ Benedetto and AI Zayed Sampling Theory Wavelets and Tomography(Birkhaumluser Boston Basel Berlin 2004)

[Ben07] I Bengtsson K Zyczkowski Geometry of Quantum States An Introduction toQuantum Entanglement (Cambridge University Press Cambridge 2007)

[Ber66] SK Berberian Notes on Spectral Theory (Van Nostrand Princeton NJ 1966)

ST Ali et al Coherent States Wavelets and Their Generalizations Theoreticaland Mathematical Physics DOI 101007978-1-4614-8535-3copy Springer Science+Business Media New York 2014

541

542 References

[Ber99] JC van den Berg (ed) Wavelets in Physics (Cambridge University Press Cambridge1999)

[Ber98] G Bernuau Proprieacuteteacutes spectrales et geacuteomeacutetriques des quasicristaux Ondelettesadapteacutees aux quasicristaux Thegravese de Doctorat CEREMADE Universiteacute Paris IXDauphine France 1998

[Bie81] L Biedenharn JD Louck The Racah-Wigner Algebra in Quantum Theory Ency-clopaedia of Mathematics vol 9 (Addison-Wesley Reading MA 1981)

[Bis10] S Biskri Deacutetection et analyse des boucles magneacutetiques solaires par traitementdrsquoimages Thegravese de Doctorat UST Houari Boumediegravene Alger 2010

[Bog05] I Bogdanova Wavelets on non-Euclidean manifolds PhD thesis EPFL 2005[Bog74] J Bognar Indefinite Inner Product Spaces (Springer Berlin 1974)[Bor72] A Borel Repreacutesentations des groupes localement compacts Lecture Notes in

Mathematics vol 276 (Springer Berlin 1972)[Bou93] K Bouyoucef Sur des aspects multireacutesolution en reconstruction drsquoimages Applica-

tion au Teacutelescope Spatial de Hubble Thegravese de Doctorat Univ P Sabatier Toulouse1993

[Bou97] A Bouzouina Comportement semi-classique de symplectomorphismes du tore quan-tifieacutes Thegravese de Doctorat Univ Paris-Dauphine 1997

[Bus91] P Busch PJ Lahti P Mittelstaedt The Quantum Theory of Measurement (SpringerBerlin and Heidelberg 1991)

[Can98] EJ Candegraves Ridgelets Theory and applications PhD thesis Department of Statis-tics Stanford University 1998

[Chr03] O Christensen An Introduction to Frames and Riesz Bases (Birkhaumluser BaselBoston Berlin 2003)

[Chu92] CK Chui An Introduction to Wavelets (Academic San Diego 1992)[Coh77] C Cohen-Tannoudji B Diu F Laloeuml Meacutecanique Quantique Tome I (Hermann

Paris 1977)[Com90] J-M Combes A Grossmann P Tchamitchian (eds) Wavelets Time-Frequency

Methods and Phase Space (Proc Marseille 1987) 2nd edn (Springer Berlin 1990)[Com12] M Combescure D Robert Shape Analysis and Classification Theory and Practice

(Springer Dordrecht Heidelberg 2012)[Cos01] LF Costa RM Cesar Jr Coherent States and Applications in Mathematical Physics

(CRC Press Boca Raton FL 2001)[Dau92] I Daubechies Ten Lectures on Wavelets (SIAM Philadelphia 1992)[Dav90] EB Davies Heat Kernels and Spectral Theory (Cambridge University Press Cam-

bridge 1990)[DeV88] R De Valois K De Valois Spatial Vision (Oxford University Press New York 1988)

[Dir01] PAM Dirac Lectures on Quantum Mechanics (Dover New York 2001)[Dix64] J Dixmier Les C-algegravebres et leurs repreacutesentations (Gauthier-Villars Paris 1964)[Dod03] VV Dodonov VI Manrsquoko (eds) Theory of Nonclassical States of Light (Taylor and

Francis London New York 2003)[Duv91] M Duval-Destin Analyse spatiale et spatio-temporelle de la stimulation visuelle agrave

lrsquoaide de la transformeacutee en ondelettes Thegravese de Doctorat Universiteacute drsquoAix-MarseilleII 1991

[Fea90] J-C Feauveau Analyse multireacutesolution par ondelettes non orthogonales et bancs defiltres numeacuteriques Thegravese de Doctorat Universiteacute Paris-Sud 1990

[Fei98] HG Feichtinger T Strohmer (eds) Gabor Analysis and Algorithms ndash Theory andApplications (Birkhaumluser Boston-Basel-Berlin 1998)

[Fei01] HG Feichtinger T Strohmer (eds) Advances in Gabor Analysis (BirkhaumluserBoston 2001)

[Fen94] DH Feng JR Klauder M Strayer (eds) Coherent States Past Present and Future(Proc Oak Ridge 1993) (World Scientific Singapore 1994)

[Fla98] P Flandrin Temps-Freacutequence (Hermegraves Paris 1993) Engliah translation Time-FrequencyTime-Scale Analysis (Academic New York 1998)

References 543

[Fol95] GB Folland A Course in Abstract Harmonic Analysis (CRC Press Boca Raton FL1995)

[Fre97] W Freeden M Schreiner T Gervens Constructive Approximation on the Spherewith Applications to Geomathematics (Clarendon Press Oxford 1997)

[Fue05] H Fuumlhr Abstract Harmonic Analysis of Continuous Wavelet Transforms LectureNotes in Mathematics vol 1863 (Springer Berlin Heidelberg 2005)

[Gaa73] SA Gaal Linear Analysis and Representation Theory (Springer Berlin 1973)[Gaz09] J-P Gazeau Coherent States in Quantum Physics (Wiley-VCH Berlin 2009)[Gel64] IM Gelfand NY Vilenkin Generalized Functions vol 4 (Academic New York

1964)[Gen13] G Gentili C Stoppato DC Struppa Regular Functions for a Quaternionic Variable

Springer Monographs in Mathematics (Springer Berlin 2013)[Gol81] H Goldstein C Poole J Safko Classical Mechanics 3rd edn (Addison-Wesley

Reading MA 1981)[Got66] K Gottfried Quantum Mechanics Fundamentals vol I (Benjamin New York and

Amsterdam 1966)[Grouml01] K Groumlchenig Foundations of Time-Frequency Analysis (Birkhaumluser Boston 2001)[Gun94] H Guumlnther NMR Spectroscopy 2nd edn (Wiley Chichester New York 1994)[Gui84] V Guillemin S Sternberg Symplectic Techniques in Physics (Cambridge University

Press Cambridge 1984)[Hei06] C Heil D Walnut (eds) Fundamental Papers in Wavelet Theory (Princeton Univer-

sity Press Princeton NJ 2006)[Hel78] S Helgason Differential Geometry Lie Groups and Symmetric Spaces (Academic

New York 1978)[Hel76] CW Helstrom Quantum Detection and Estimation Theory (Academic New York

1976)[Her89] G Herzberg Molecular Spectra and Molecular Structure Spectra of Diatomic

Molecules 2nd edn (Krieger Pub Malabar FL 1989)[Hil71] P Hilton U Stammbach A Course in Homological Algebra (Springer Berlin 1971)[H0l01] AS Holevo Statistical Structure of Quantum Theory (Springer Berlin 2001)[Hol95] M Holschneider Wavelets An Analysis Tool (Oxford University Press Oxford 1995)[Hon07] G Honnouvo Gabor analysis and wavelet transforms on some non-Euclidean 2-

dimensional manifolds PhD thesis Concordia University Montreal PQ Canada2007

[Hua63] LK Hua Harmonic Analysis of Functions of Several Complex Variables in the Clas-sical Domains Translations of Mathematical Monographs (American MathematicalSociety Providence RI 1963)

[Hum72] JE Humphreys Introduction to Lie Algebras and Representation Theory (SpringerBerlin 1972)

[Inouml54] E Inoumlnuuml A study of the unitary representations of the Galilei group in relation toquantum mechanics PhD thesis University of Ankara 1954

[Ino92] A Inomata H Kuratsuji CC Gerry Path Integrals and Coherent States of SU(2)and SU(11) (World Scientific Singapore 1992)

[Jac62] N Jacobson Lie Algebras (Interscience New York and London 1962)[Jac04] L Jacques Ondelettes repegraveres et couronne solaire Thegravese de Doctorat Univ Cath

Louvain Louvain-la-Neuve 2004[Jaf96] S Jaffard Y Meyer Wavelet Methods for Pointwise Regularity and Local Oscillations

of Functions Memoirs of the American Mathematical Society vol 143 (AmericanMathematical Society Providence RI 1996)

[Kah98] J-P Kahane PG Lemarieacute-Rieusset Fourier Series and Wavelets (Gordon and BreachLuxembourg 1995) French translation Seacuteries de Fourier et ondelettes (Cassini Paris1998)

[Kai94] G Kaiser A Friendly Guide to Wavelets (Birkhaumluser Boston 1994)[Kat76] T Kato Perturbation Theory for Linear Operators (Springer Berlin 1976)

544 References

[Kem37] EC Kemble Fundamental Principles of Quantum Mechanics (McGraw Hill NewYork 1937)

[Kir76] AA Kirillov Elements of the Theory of Representations (Springer Berlin 1976)[Kla68] JR Klauder ECG Sudarshan Fundamentals of Quantum Optics (Benjamin New

York 1968)[Kla85] JR Klauder BS Skagerstam Coherent States ndash Applications in Physics and

Mathematical Physics (World Scientific Singapore 1985)[Kla00] JR Klauder Beyond Conventional Quantization (Cambridge University Press Cam-

bridge 2000)[Kla11] JR Klauder A Modern Approach to Functional Integration (BirkhaumluserSpringer

New York 2011)[Kna96] AW Knapp Lie Groups Beyond an Introduction (Birkhaumluser Basel 1996 2nd edn

2002)[Kut12] G Kutyniok D Labate (eds) Shearlets Multiscale Analysis for Multivariate Data

(Birkhaumluser Boston 2012)[Lan81] L Landau E Lifchitz Mechanics 3rd edn (Pergamon Oxford1981)[Lan93] S Lang Algebra 3rd edn (Addison-Wesley Reading MA 1993)[Lie97] EH Lieb M Loss Analysis (American Mathematical Society Providence RI 1997)[Lip74] RL Lipsman Group Representations Lecture Notes in Mathematics vol 388

(Springer Berlin 1974)[Lyn82] PA Lynn An Introduction to the Analysis and Processing of Signals 2nd edn

(MacMillan London 1982)[Mac68] GW Mackey Induced Representations of Groups and Quantum Mechanics (Ben-

jamin New York 1968)[Mac76] GW Mackey Theory of Unitary Group Representations (University of Chicago

Press Chicago 1976)[Mad95] J Madore An Introduction to Noncommutative Differential Geometry and Its Physical

Applications (Cambridge University Press Cambridge 1995)[Mae94] S Maes The wavelet transform in signal processing with application to the extraction

of the speech modulation model features Thegravese de Doctorat Univ Cath LouvainLouvain-la-Neuve 1994

[Mag66] W Magnus F Oberhettinger RP Soni Formulas and Theorems for the SpecialFunctions of Mathematical Physics (Springer Berlin 1966)

[Mal99] SG Mallat A Wavelet Tour of Signal Processing 2nd edn (Academic San Diego1999)

[Mar82] D Marr Vision (Freeman San Francisco 1982)[Mes62] H Meschkowsky Hilbertsche Raumlume mit Kernfunktionen (Springer Berlin 1962)[Mey91] Y Meyer (ed) Wavelets and Applications (Proc Marseille 1989) (Masson and

Springer Paris and Berlin 1991)[Mey92] Y Meyer Les Ondelettes Algorithmes et Applications (Armand Colin Paris 1992)

English translation Wavelets Algorithms and Applications (SIAM Philadelphia1993)

[Mey00] CD Meyer Matrix Analysis and Applied Linear Algebra (SIAM Philadelphia 2000)[Mey93] Y Meyer S Roques (eds) Progress in Wavelet Analysis and Applications (Proc

Toulouse 1992) (Ed Frontiegraveres Gif-sur-Yvette 1993)[Mur90] R Murenzi Ondelettes multidimensionnelles et applications agrave lrsquoanalyse drsquoimages

Thegravese de Doctorat Univ Cath Louvain Louvain-la-Neuve 1990[vNe55] J von Neumann Mathematical Foundations of Quantum Mechanics (Princeton

University Press Princeton NJ 1955) (English translated by RT Byer)[Pap02] A Papoulis SU Pillai Probability Random Variables and Stochastic Processes 4th

edn (McGraw Hill New York 2002)[Par05] KR Parthasarathy Probability Measures on Metric Spaces (AMS Chelsea Publish-

ing Providence RI 2005)

References 545

[Pau85] T Paul Ondelettes et Meacutecanique Quantique Thegravese de doctorat Univ drsquoAix-MarseilleII 1985

[Per86] AM Perelomov Generalized Coherent States and Their Applications (SpringerBerlin 1986)

[Per05] G Peyreacute Geacuteomeacutetrie multi-eacutechelles pour les images et les textures Thegravese de doctoratEcole Polytechnique Palaiseau 2005

[Pru86] E Prugovecki Stochastic Quantum Mechanics and Quantum Spacetime (ReidelDordrecht 1986)

[Rau04] H Rauhut Time-frequency and wavelet analysis of functions with symmetry proper-ties PhD thesis TU Muumlnich 2004

[Ree80] M Reed B Simon Methods of Modern Mathematical Physics I Functional Analysis(Academic New York 1980)

[Rud62] W Rudin Fourier Analysis on Groups (Interscience New York 1962)[Sch96] FE Schroeck Jr Quantum Mechanics on Phase Space (Kluwer Dordrecht 1996)[Sch61] L Schwartz Meacutethodes matheacutematiques pour les sciences physiques (Hermann Paris

1961)[Scu97] MO Scully MS Zubairy Quantum Optics (Cambridge University Press Cam-

bridge 1997)[Sho50] JA Shohat JD Tamarkin The Problem of Moments (American Mathematical

Society Providence RI 1950)[Ste71] EM Stein G Weiss Introduction to Fourier Analysis on Euclidean Spaces (Prince-

ton University Press Princeton NJ 1971)[Str64] RF Streater AS Wightman PCT Spin and Statistics and All That (Benjamin New

York 1964)[Sug90] M Sugiura Unitary Representations and Harmonic Analysis An Introduction

(North-HollandKodansha Ltd Tokyo 1990)[Suv11] A Suvichakorn C Lemke A Schuck Jr J-P Antoine The continuous wavelet

transform in MRS Tutorial text Marie Curie Research Training Network FAST(2011) httpwwwfast-mariecurie-rtn-projecteuWavelet

[Tak79] M Takesaki Theory of Operator Algebras I (Springer New York 1979)[Ter88] A Terras Harmonic Analysis on Symmetric Spaces and Applications II (Springer

Berlin 1988)[Tho98] G Thonet New aspects of time-frequency analysis for biomedical signal processing

Thegravese de Doctorat EPFL Lausanne 1998[Tor95] B Torreacutesani Analyse continue par ondelettes (InterEacuteditionsCNRS Eacuteditions Paris

1995)[Unt87] A Unterberger Analyse harmonique et analyse pseudo-diffeacuterentielle du cocircne de

lumiegravere Asteacuterisque 156 1ndash201 (1987)[Unt91] A Unterberger Quantification relativiste Meacutem Soc Math France 44ndash45 1ndash215

(1991)[Van98] P Vandergheynst Ondelettes directionnelles et ondelettes sur la sphegravere Thegravese de

Doctorat Univ Cath Louvain Louvain-la-Neuve 1998[Var85] VS Varadarajan Geometry of Quantum Theory 2nd edn (Springer New York 1985)[Vet95] M Vetterli J Kovacevic Wavelets and Subband Coding (Prentice Hall Englewood

Cliffs NJ 1995)[Vil69] NJ Vilenkin Fonctions speacuteciales et theacuteorie de la repreacutesentation des groupes (Dunod

Paris 1969)[Wel03] GV Welland Beyond Wavelets (Academic New York 2003)[vWe86] C von Westenholz Differential Forms in Mathematical Physics (North-Holland

Amsterdam 1986)[Wey28] H Weyl Gruppentheorie und Quantenmechanik (Hirzel Leipzig 1928)[Wey31] H Weyl The Theory of Groups and Quantum Mechanics (Dover New York 1931)[Wic94] MV Wickerhauser Adapted Wavelet Analysis from Theory to Software (A K Peters

Wellesley MA 1994)

546 References

[Wis93] W Wisnoe Utilisation de la meacutethode de transformeacutee en ondelettes 2D pour lrsquoanalysede visualisation drsquoeacutecoulements Thegravese de Doctorat ENSAE Toulouse 1993

[Woj97] P Wojtaszczyk A Mathematical Introduction to Wavelets (Cambridge UniversityPress Cambridge 1997)

[Woo92] NJM Woodhouse Geometric Quantization 2nd edn (Clarendon Press Oxford1992)

[Zac06] C Zachos D Fairlie T Curtright Quantum Mechanics in Phase Space An OverviewWith Selected Papers (World Scientific Publishing Singapore 2006)

B Articles

[1] P Abry R Baraniuk P Flandrin R Riedi D Veitch Multiscale nature of network trafficIEEE Signal Process Mag 19 28ndash46 (2002)

[2] MD Adams The JPEG-2000 still image compression standardhttpwwweceuvicca~frodopublicationsjpeg2000pdf

[3] SL Adler AC Millard Coherent states in quaternionic quantum mechanics J MathPhys 38 2117ndash2126 (1997)

[4] GS Agarwal K Tara Nonclassical properties of states generated by the excitation on acoherent state Phys Rev A 43 492ndash497 (1991)

[5] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics I Mapping theorems and ordering of func-tions of noncommuting operators Phys Rev D 2 2161ndash2186 (1970)

[6] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics II Quantum mechanics in phase space PhysRev D 2 2187ndash2205 (1970)

[7] GS Agarwal E Wolf Calculus for functions of noncommuting operators and generalphase-space methods in quantum mechanics III A generalized Wick theorem and multi-time mapping Phys Rev D 2 2206ndash2225 (1970)

[8] V Aldaya J Guerrero G Marmo Quantization on a Lie group Higher-order polariza-tions in Symmetry in Sciences X ed by B Gruber M Ramek (Plenum Press Nerw York1998) pp 1ndash36

[9] M Alexandrescu D Gibert G Hulot J-L Le Mouel G Saracco Worldwide waveletanalysis of geomagnetic jerks J Geophys Res B 101 21975ndash21994 (1996)

[10] G Alexanian A Pinzul A Stern Generalized coherent state approach to star productsand applications to the fuzzy sphere Nucl Phys B 600 531ndash547 (2001)

[11] ST Ali A geometrical property of POV-measures and systems of covariance in Differ-ential Geometric Methods in Mathematical Physics ed by HD Doebner SI AnderssonHR Petry Lecture Notes in Mathematics vol 905 (Springer Berlin 1982) pp 207ndash22

[12] ST Ali Commutative systems of covariance and a generalization of Mackeyrsquos imprimi-tivity theorem Canad Math Bull 27 390ndash397 (1984)

[13] ST Ali Stochastic localisation quantum mechanics on phase space and quantum space-time Riv Nuovo Cim 8(11) 1ndash128 (1985)

[14] ST Ali A general theorem on square-integrability Vector coherent states J Math Phys39 3954ndash3964 (1998)

[15] ST Ali J-P Antoine Coherent states of 1+1 dimensional Poincareacute group Squareintegrability and a relativistic Weyl transform Ann Inst H Poincareacute 51 23ndash44 (1989)

[16] ST Ali S De Biegravevre Coherent states and quantization on homogeneous spaces in GroupTheoretical Methods in Physics ed by H-D Doebner et al Lecture Notes in Mathematicsvol 313 (Springer Berlin 1988) pp 201ndash207

References 547

[17] ST Ali H-D Doebner Ordering problem in quantum mechanics Prime quantization anda physical interpretation Phys Rev A 41 1199ndash1210 (1990)

[18] ST Ali GG Emch Geometric quantization Modular reduction theory and coherentstates J Math Phys 27 2936ndash2943 (1986)

[19] ST Ali M Engliš J-P Gazeau Vector coherent states from Plancherelrsquos theorem andClifford algebras J Phys A 37 6067ndash6089 (2004)

[20] ST Ali MEH Ismail Some orthogonal polynomials arising from coherent states JPhys A 45 125203 (2012) (16pp)

[21] ST Ali UA Mueller Quantization of a classical system on a coadjoint orbit of thePoincareacute group in 1+1 dimensions J Math Phys 35 4405ndash4422 (1994)

[22] ST Ali E Prugovecki Systems of imprimitivity and representations of quantum mechan-ics on fuzzy phase spaces J Math Phys 18 219ndash228 (1977)

[23] ST Ali E Prugovecki Mathematical problems of stochastic quantum mechanics Har-monic analysis on phase space and quantum geometry Acta Appl Math 6 1ndash18 (1986)

[24] ST Ali E Prugovecki Extended harmonic analysis of phase space representation for theGalilei group Acta Appl Math 6 19ndash45 (1986)

[25] ST Ali E Prugovecki Harmonic analysis and systems of covariance for phase spacerepresentation of the Poincareacute group Acta Appl Math 6 47ndash62 (1986)

[26] ST Ali J-P Antoine J-P Gazeau De Sitter to Poincareacute contraction and relativisticcoherent states Ann Inst H Poincareacute 52 83ndash111 (1990)

[27] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces I Reproducing triples and frames Ann Inst H Poincareacute 55 829ndash855 (1991)

[28] ST Ali J-P Antoine J-P Gazeau Square integrability of group representations onhomogeneous spaces II Coherent and quasi-coherent states The case of the Poincareacutegroup Ann Inst H Poincareacute 55 857ndash890 (1991)

[29] ST Ali J-P Antoine J-P Gazeau Continuous frames in Hilbert space Ann Phys(NY)222 1ndash37 (1993)

[30] ST Ali J-P Antoine J-P Gazeau Relativistic quantum frames Ann Phys(NY) 222 38ndash88 (1993)

[31] ST Ali J-P Antoine J-P Gazeau UA Mueller Coherent states and their generalizationsA mathematical overview Rev Math Phys 7 1013ndash1104 (1995)

[32] ST Ali J-P Gazeau MR Karim Frames the β -duality in Minkowski space and spincoherent states J Phys A Math Gen 29 5529ndash5549 (1996)

[33] ST Ali M Engliš Quantization methods A guide for physicists and analysts Rev MathPhys 17 391ndash490 (2005)

[34] ST Ali J-P Gazeau B Heller Coherent states and Bayesian duality J Phys A MathTheor 41 365302 (2008)

[35] ST Ali L Balkovaacute EMF Curado J-P Gazeau MA Rego-Monteiro LMCSRodrigues K Sekimoto Non-commutative reading of the complex plane through Delonesequences J Math Phys 50 043517 (2009)

[36] ST Ali C Carmeli T Heinosaari A Toigo Commutative POVMS and fuzzy observ-ables Found Phys 39 593ndash612 (2009)

[37] ST Ali T Bhattacharyya SS Roy Coherent states on Hilbert modules J Phys A MathTheor 44 275202 (2011)

[38] ST Ali J-P Antoine F Bagarello J-P Gazeau (Guest Editors) Coherent states Acontemporary panorama preface to a special issue on Coherent states Mathematical andphysical aspects J Phys A Math Gen 45(24) (2012)

[39] ST Ali F Bagarello J-P Gazeau Quantizations from reproducing kernel spaces AnnPhys (NY) 332 127ndash142 (2013)

[40] STAli K Goacuterska A Horzela F Szafraniec Squeezed states and Hermite polynomials ina complex variable Preprint (2013) arXiv13084730v1 [quant-phy]

[41] P Aniello G Cassinelli E De Vito A Levrero Square-integrability of induced represen-tations of semidirect products Rev Math Phys 10 301ndash313 (1998)

548 References

[42] P Aniello G Cassinelli E De Vito A Levrero Wavelet transforms and discrete framesassociated to semidirect products J Math Phys 39 3965ndash3973 (1998)

[43] J-P Antoine Remarques sur le vecteur de Runge-Lenz Ann Soc Scient Bruxelles 80160ndash168 (1966)

[44] J-P Antoine Etude de la deacutegeacuteneacuterescence orbitale du potentiel coulombien en theacuteorie desgroupes I II Ann Soc Scient Bruxelles 80 169ndash184 (1966)


[46] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics I Generaldirac formalism J Math Phys 10 53ndash69 (1969)

[47] J-P Antoine Dirac formalism and symmetry problems in quantum mechanics II Symme-try problems J Math Phys 10 2276ndash2290 (1969)

[48] J-P Antoine Quantum mechanics beyond Hilbert space in Irreversibility and Causality mdashSemigroups and Rigged Hilbert Spaces ed by A Boumlhm H-D Doebner P KielanowskiLecture Notes in Physics vol 504 (Springer Berlin 1998) pp 3ndash33

[49] J-P Antoine Discrete wavelets on abelian locally compact groups Rev Cien Math(Habana) 19 3ndash21 (2003)

[50] J-P Antoine Introduction to precursors in physics Affine coherent states in FundamentalPapers in Wavelet Theory ed by C Heil D Walnut (Princeton University Press PrincetonNJ 2006) pp 113ndash116

[51] J-P Antoine F Bagarello Wavelet-like orthonormal bases for the lowest Landau levelJ Phys A Math Gen 27 2471ndash2481 (1994)

[52] J-P Antoine P Balazs Frames and semi-frames J Phys A Math Theor 44 205201(2011) (25 pages) Corrigendum J-P Antoine P Balazs Frames and semi-frames J PhysA Math Theor 44 479501 (2011) (2 pages)

[53] J-P Antoine P Balazs Frames semi-frames and Hilbert scales Numer Funct AnalOptim 33 736ndash769 (2012)

[54] J-P Antoine A Coron Time-frequency and time-scale approach to magnetic resonancespectroscopy J Comput Methods Sci Eng (JCMSE) 1 327ndash352 (2001)

[55] J-P Antoine AL Hohoueacuteto Discrete frames of Poincareacute coherent states in 1+3 dimen-sions J Fourier Anal Appl 9 141ndash173 (2003)

[56] J-P Antoine I Mahara Galilean wavelets Coherent states for the affine Galilei groupJ Math Phys 40 5956ndash5971 (1999)

[57] J-P Antoine U Moschella Poincareacute coherent states The two-dimensional massless caseJ Phys A Math Gen 26 591ndash607 (1993)

[58] J-P Antoine R Murenzi Two-dimensional directional wavelets and the scale-anglerepresentation Signal Process 52 259ndash281 (1996)

[59] J-P Antoine R Murenzi Two-dimensional continuous wavelet transform as linear phasespace representation of two-dimensional signals in Wavelet Applications IV SPIE Pro-ceedings vol 3078 (SPIE Bellingham WA 1997) pp 206ndash217

[60] J-P Antoine D Rosca The wavelet transform on the two-sphere and related manifolds mdashA review in Optical and Digital Image Processing SPIE Proceedings vol 7000 (2008)pp 70000B-1ndash15

[61] J-P Antoine D Speiser Characters of irreducible representations of simple Lie groupsJ Math Phys 5 1226ndash1234 (1964)

[62] J-P Antoine P Vandergheynst Wavelets on the n-sphere and related manifolds J MathPhys 39 3987ndash4008 (1998)

[63] J-P Antoine P Vandergheynst Wavelets on the 2-sphere A group-theoretical approachAppl Comput Harmon Anal 7 262ndash291 (1999)

[64] J-P Antoine P Vandergheynst Wavelets on the two-sphere and other conic sections JFourier Anal Appl 13 369ndash386 (2007)

[65] J-P Antoine M Duval-Destin R Murenzi B Piette Image analysis with 2D wavelettransform Detection of position orientation and visual contrast of simple objects inWavelets and Applications (Proc Marseille 1989) ed by Y Meyer (Masson and SpringerParis and Berlin 1991) pp144ndash159

References 549

[66] J-P Antoine P Carrette R Murenzi B Piette Image analysis with 2D continuous wavelettransform Signal Process 31 241ndash272 (1993)

[67] J-P Antoine P Vandergheynst K Bouyoucef R Murenzi Alternative representations ofan image via the 2D wavelet transform Application to character recognition in VisualInformation Processing IV SPIE Proceedings vol 2488 (SPIE Bellingham WA 1995)pp 486ndash497

[68] J-P Antoine R Murenzi P Vandergheynst Two-dimensional directional wavelets inimage processing Int J Imaging Syst Tech 7 152ndash165 (1996)

[69] J-P Antoine D Barache RM Cesar Jr LF Costa Shape characterization with thewavelet transform Signal Process 62 265ndash290 (1997)

[70] J-P Antoine P Antoine B Piraux Wavelets in atomic physics in Spline Functions andthe Theory of Wavelets ed by S Dubuc G Deslauriers CRM Proceedings and LectureNotes vol 18 (AMS Providence RI 1999) pp261ndash276

[71] J-P Antoine P Antoine B Piraux Wavelets in atomic physics and in solid state physicsin Wavelets in Physics Chap 8 ed by JC van den Berg (Cambridge University PressCambridge 1999)

[72] J-P Antoine R Murenzi P Vandergheynst Directional wavelets revisited Cauchywavelets and symmetry detection in patterns Appl Comput Harmon Anal 6 314ndash345(1999)

[73] J-P Antoine L Jacques R Twarock Wavelet analysis of a quasiperiodic tiling withfivefold symmetry Phys Lett A 261 265ndash274 (1999)

[74] J-P Antoine L Jacques P Vandergheynst Penrose tilings quasicrystals and wavelets inWavelet Applications in Signal and Image Processing VII SPIE Proceedings vol 3813(SPIE Bellingham WA 1999) pp 28ndash39

[75] J-P Antoine YB Kouagou D Lambert B Torreacutesani An algebraic approach to discretedilations Application to discrete wavelet transforms J Fourier Anal Appl 6 113ndash141(2000)

[76] J-P Antoine A Coron J-M Dereppe Water peak suppression Time-frequency vs time-scale approach J Magn Reson 144 189ndash194 (2000)

[77] J-P Antoine J-P Gazeau P Monceau J R Klauder K Penson Temporally stablecoherent states for infinite well and Poumlschl-Teller potentials J Math Phys 42 2349ndash2387(2001)

[78] J-P Antoine A Coron C Chauvin Wavelets and related time-frequency techniques inmagnetic resonance spectroscopy NMR Biomed 14 265ndash270 (2001)

[79] J-P Antoine L Demanet J-F Hochedez L Jacques R Terrier E Verwichte Applicationof the 2-D wavelet transform to astrophysical images Phys Mag 24 93ndash116 (2002)

[80] J-P Antoine L Demanet L Jacques P Vandergheynst Wavelets on the sphere Imple-mentation and approximations Appl Comput Harmon Anal 13 177ndash200 (2002)

[81] J-P Antoine I Bogdanova P Vandergheynst The continuous wavelet transform on conicsections Int J Wavelets Multires Inform Proc 6 137ndash156 (2007)

[82] J-P Antoine D Rosca P Vandergheynst Wavelet transform on manifolds Old and newapproaches Appl Comput Harmon Anal 28 189ndash202 (2010)

[83] P Antoine B Piraux A Maquet Time profile of harmonics generated by a single atom ina strong electromagnetic field Phys Rev A 51 R1750ndashR1753 (1995)

[84] P Antoine B Piraux DB Miloševic M Gajda Generation of ultrashort pulses ofharmonics Phys Rev A 54 R1761ndashR1764 (1996)

[85] P Antoine B Piraux DB Miloševic M Gajda Temporal profile and time control ofharmonic generation Laser Phys 7 594ndash601 (1997)

[86] Apollonius see Wikipedia httpenwikipediaorgwikiApollonius_of_Perga[87] FT Arecchi E Courtens R Gilmore H Thomas Atomic coherent states in quantum

optics Phys Rev A 6 2211ndash2237 (1972)[88] I Aremua J-P Gazeau MN Hounkonnou Action-angle coherent states for quantum

systems with cylindric phase space J Phys A Math Theor 45 335302 (2012)

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[90] F Argoul A Arneacuteodo J Elezgaray G Grasseau R Murenzi Wavelet analysis of theself-similarity of diffusion-limited aggregates and electrodeposition clusters Phys Rev A41 5537ndash5560 (1990)

[91] TA Arias Multiresolution analysis of electronic structure Semicardinal and waveletbases Rev Mod Phys 71 267ndash312 (1999)

[92] A Arneacuteodo F Argoul E Bacry J Elezgaray E Freysz G Grasseau JF Muzy BPouligny Wavelet transform of fractals in Wavelets and Applications (Proc Marseille1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 286ndash352

[93] A Arneacuteodo E Bacry JF Muzy The thermodynamics of fractals revisited with waveletsPhysica A 213 232ndash275 (1995)

[94] A Arneacuteodo E Bacry JF Muzy Oscillating singularities in locally self-similar functionsPhys Rev Lett 74 4823ndash4826 (1995)

[95] A Arneacuteodo E Bacry PV Graves JF Muzy Characterizing long-range correlations inDNA sequences from wavelet analysis Phys Rev Lett 74 3293ndash3296 (1996)

[96] A Arneacuteodo Y drsquoAubenton E Bacry PV Graves JF Muzy C Thermes Wavelet basedfractal analysis of DNA sequences Physica D 96 291ndash320 (1996)

[97] A Arneacuteodo E Bacry S Jaffard JF Muzy Oscillating singularities on Cantor sets Agrand canonical multifractal formalism J Stat Phys 87 179ndash209 (1997)

[98] A Arneacuteodo E Bacry S Jaffard JF Muzy Singularity spectrum of multifractal functionsinvolving oscillating singularities J Fourier Anal Appl 4 159ndash174 (1998)

[99] N Aronszajn Theory of reproducing kernels Trans Amer Math Soc 66 337ndash404 (1950)[100] A Ashtekar J Lewandowski D Marolf J Mouratildeo T Thiemann Coherent state

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206ndash211 (1968)[103] EW Aslaksen JR Klauder Continuous representation theory using the affine group

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wavelet transform for the analysis of computational fluid dynamics results in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 463ndash470

[105] PW Atkins JC Dobson Angular momentum coherent states Proc Roy Soc London A321 321ndash340 (1971)

[106] BW Atkinson DO Bruff JS Geronimo D P Hardin Wavelets centered on a knotsequence Piecewise polynomial wavelets on a quasi-crystal lattice preprint (2011)arXiv11024246v1 [mathNA]

[107] IS Averbuch NF Perelman Fractional revivals Universality in the long-term evolutionof quantum wave packets beyond the correspondence principle dynamics Phys Lett A139 449ndash453 (1989)

[108] H Bacry J-M Leacutevy-Leblond Possible kinematics J Math Phys 9 1605ndash1614 (1968)[109] H Bacry A Grossmann J Zak Proof of the completeness of lattice states in kq

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Amer Math Soc 72 593ndash600 (1978)[111] VG Bagrov J-P Gazeau D Gitman A Levine Coherent states and related quantizations

for unbounded motions J Phys A Math Theor 45 125306 (2012) arXiv12010955v2[quant-ph]

[112] P Balazs J-P Antoine A Grybos Weighted and controlled frames Mutual relationshipand first numerical properties Int J Wavelets Multires Inform Proc 8 109ndash132 (2010)

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[114] P Balazs D Bayer A Rahimi Multipliers for continuous frames in Hilbert spaces JPhys A Math Gen 45 244023 (2012)

[115] P Baldi G Kerkyacharian D Marinucci D Picard High frequency asymptotics forwavelet-based tests for Gaussianity and isotropy on the torus J Multivar Anal 99 606ndash636 (2008)

[116] P Baldi G Kerkyacharian D Marinucci D Picard Asymptotics for spherical needletsAnn of Stat 37 1150ndash1171 (2009)

[117] MC Baldiotti J-P Gazeau DM Gitman Coherent states of a particle in magnetic fieldand Stieltjes moment problem Phys Lett A 373 1916ndash1920 (2009) Erratum Phys LettA 373 2600 (2009)

[118] MC Baldiotti J-P Gazeau DM Gitman Semiclassical and quantum description ofmotion on the noncommutative plane Phys Lett A 373 3937ndash3943 (2009)

[119] R Balian Un principe drsquoincertitude fort en theacuteorie du signal ou en meacutecanique quantiqueCR Acad Sci(Paris) 292 1357ndash1362 (1981)

[120] M Bander C Itzykson Group theory and the hydrogen atom I II Rev Mod Phys 38330ndash345 346ndash358 (1966)

[121] D Barache S De Biegravevre J-P Gazeau Affine symmetry semigroups for quasicrystalsEurophys Lett 25 435ndash440 (1994)

[122] D Barache J-P Antoine J-M Dereppe The continuous wavelet transform a tool for NMRspectroscopy J Magn Reson 128 1ndash11 (1997)

[123] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart I Commun Pure Appl Math 14 187ndash214 (1961)

[124] V Bargmann On a Hilbert space of analytic functions and an associated integral transformPart II A family of related function spaces Application to distribution theory CommunPure Appl Math 20 1ndash101 (1967)

[125] V Bargmann P Butera L Girardello JR Klauder On the completeness of coherentstates Reports Math Phys 2 221ndash228 (1971)

[126] AO Barut L Girardello New ldquocoherentrdquo states associated with non compact groupsCommun Math Phys 21 41ndash55 (1971)

[127] AO Barut H Kleinert Transition probabilities of the hydrogen atom from noncompactdynamical groups Phys Rev 156 1541ndash1545 (1967)

[128] AO Barut BW Xu Non-spreading coherent states riding on Kepler orbits Helv PhysActa 66 711ndash720 (1993)

[129] G Battle Wavelets A renormalization group point of view in Wavelets and TheirApplications ed by MB Ruskai G Beylkin R Coifman I Daubechies S Mallat YMeyer L Raphael (Jones and Bartlett Boston 1992) pp 323ndash349

[130] P Bellomo CR Stroud Jr Dispersion of Klauderrsquos temporally stable coherent states forthe hydrogen atom J Phys A Math Gen 31 L445ndashL450 (1998)

[131] J Ben Geloun J R Klauder Ladder operators and coherent states for continuous spectraJ Phys A Math Theor 42 375209 (2009)

[132] J Ben Geloun J Hnybida JR Klauder Coherent states for continuous spectrum operatorswith non-normalizable fiducial states J Phys A Math Theor 45 085301 (2012)

[133] JJ Benedetto TD Andrews Intrinsic wavelet and frame applications in IndependentComponent Analyses Wavelets Neural Networks Biosystems and Nanoengineering IXed by H Szu L Dai SPIE Proceedings vol 8058 (SPIE Bellingham WA 2011) p805802

[134] JJ Benedetto A Teolis A wavelet auditory model and data compression Appl ComputHarmon Anal 1 3ndash28 (1993)

[135] FA Berezin Quantization Math USSR Izvestija 8 1109ndash1165 (1974)[136] FA Berezin General concept of quantization Commun Math Phys 40 153ndash174 (1975)[137] H Bergeron From classical to quantum mechanics How to translate physical ideas into

mathematical language J Math Phys 42 3983ndash4019 (2001)

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[139] H Bergeron and J-P Gazeau Integral quantization with two basic examples Preprint(2013) arXiv13082348v1

[140] H Bergeron A Valance Overcomplete basis for one dimensional Hamiltonians J MathPhys 36 1572ndash1592 (1995)

[141] H Bergeron J-P Gazeau P Siegl A Youssef Semi-classical behavior of Poumlschl-Tellercoherent states Eur Phys Lett 92 60003 (2010)

[142] H Bergeron P Siegl A Youssef New SUSYQM coherent states for Poumlschl-Tellerpotentials A detailed mathematical analysis J Phys A Math Theor 45 244028 (2012)

[143] H Bergeron J-P Gazeau A Youssef Are the Weyl and coherent state descriptionsphysically equivalent Phys Lett A 377 598ndash605 (2013)

[144] H Bergeron A Dapor J-P Gazeau P Małkiewicz Wavelet quantum cosmology preprint(2013) arXiv13050653 [gr-qc]

[145] S Bergman Uumlber die Kernfunktion eines Bereiches und ihr Verhalten am Rande I ReineAngw Math 169 1ndash42 (1933)

[146] D Bernier KF Taylor Wavelets from square-integrable representations SIAM J MathAnal 27 594ndash608 (1996)

[147] G Bernuau Wavelet bases associated to a self-similar quasicrystal J Math Phys 394213ndash4225 (1998)

[148] A Bertrand Deacuteveloppements en base de Pisot et reacutepartition modulo 1 C R Acad SciParis 285 419ndash421 (1977)

[149] J Bertrand P Bertrand Classification of affine Wigner functions via an extendedcovariance principle in Group Theoretical Methods in Physics (Proc Sainte-Adegravele 1988)ed by Y Saint-Aubin L Vinet (World Scientific Singapore 1989) pp 1380ndash1383

[150] Z Białynicka-Birula I Białynicki-Birula Space-time description of squeezing J OptSoc Am B4 1621ndash1626 (1987)

[151] E Bianchi E Magliaro C Perini Coherent spin-networks Phys Rev D 82 024012(2010)

[152] S Biskri J-P Antoine B Inhester F Mekideche Extraction of Solar coronal magneticloops with the 2-D Morlet wavelet transform Solar Phys 262 373ndash385 (2010)

[153] R Bluhm VA Kostelecky JA Porter The evolution and revival structure of localizedquantum wave packets Am J Phys 64 944ndash953 (1996)

[154] I Bogdanova P Vandergheynst J-P Antoine L Jacques M Morvidone Stereographicwavelet frames on the sphere Appl Comput Harmon Anal 19 223ndash252 (2005)

[155] I Bogdanova X Bresson J-P Thiran P Vandergheynst Scale space analysis and activecontours for omnidirectional images IEEE Trans Image Process 16 1888ndash1901 (2007)

[156] I Bogdanova P Vandergheynst J-P Gazeau Continuous wavelet transform on thehyperboloid Appl Comput Harmon Anal 23 (2007) 286ndash306 (2007)

[157] P Boggiatto E Cordero Anti-Wick quantization of tempered distributions in Progress inAnalysis Berlin (2001) vol I II (World Sci Publ River Edge NJ 2003) pp 655ndash662

[158] P Boggiatto E Cordero K Groumlchenig Generalized Anti-Wick operators with symbols indistributional Sobolev spaces Int Equ Oper Theory 48 427ndash442 (2004)

[159] A Boumlhm The Rigged Hilbert Space in quantum mechanics in Lectures in TheoreticalPhysics vol IX A ed by WA Brittin et al (Gordon amp Breach New York 1967) pp255ndash315

[160] G Bohnkeacute Treillis drsquoondelettes associeacutes aux groupes de Lorentz Ann Inst H Poincareacute54 245ndash259 (1991)

[161] WR Bomstad JR Klauder Linearized quantum gravity using the projection operatorformalism Class Quantum Grav 23 5961ndash5981 (2006)

[162] VV Borzov Orthogonal polynomials and generalized oscillator algebras Int TransformSpec Funct 12 115ndash138 (2001)

[163] VV Borzov EV Damaskinsky Generalized coherent states for classical orthogonalpolynomials Day on Diffraction (2002) arXivmathQA0209181v1 (SPb 2002)

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[165] A Bouzouina S De Biegravevre Equipartition of the eigenfunctions of quantized ergodic mapson the torus Commun Math Phys 178 83ndash105 (1996)

[166] P Brault J-P Antoine A spatio-temporal Gaussian-Conical wavelet with high apertureselectivity for motion and speed analysis Appl Comput Harmon Anal 34 148ndash161(2012)

[167] A Briguet S Cavassila D Graveron-Demilly Suppression of huge signals using theCadzow enhancement procedure The NMR Newslett 440 26 (1995)

[168] CM Brislawn Fingerprints go digital Notices Amer Math Soc 42 1278ndash1283 (1995)[169] CM Brislawn On the group-theoretic structure of lifted filter banks in Excursions in

Harmonic Analysis vol 1 2 ed by TD Andrews R Balan JJ Benedetto W CzajaKA Okoudjou (Birkhaumluser Boston 2013) pp 113ndash135

[170] F Bruhat Sur les repreacutesentations induites des groupes de Lie Bull Soc Math France 8497ndash205 (1956)

[171] T Buumllow Multiscale image processing on the sphere in DAGM-Symposium (2002) pp609ndash617

[172] C Burdik C Frougny J-P Gazeau R Krejcar Beta-integers as natural counting systemsfor quasicrystals J Phys A Math Gen 31 6449ndash6472 (1998)

[173] KE Cahill Coherent-state representations for the photon density Phys Rev 138 B1566ndash1576 (1965)

[174] KE Cahill R Glauber Density operators and quasiprobability distributions Phys Rev177 1882ndash1902 (1969)

[175] KE Cahill R Glauber Ordered expansions in boson amplitude operators Phys Rev 1771857ndash1881 (1969)

[176] AR Calderbank I Daubechies W Sweldens BL Yeo Wavelets that map integers tointegers Appl Comput Harmon Anal 5 332ndash369 (1998)

[177] M Calixto J Guerrero Wavelet transform on the circle and the real line A unified group-theoretical treatment Appl Comput Harmon Anal 21 204ndash229 (2006)

[178] M Calixto E Peacuterez-Romero Extended MacMahon-Schwingerrsquos master theorem andconformal wavelets in complex Minkowski space Appl Comput Harmon Anal 31 143ndash168 (2011)

[179] M Calixto J Guerrero D Rosca Wavelet transform on the torus A group-theoreticalapproach preprint (2013)

[180] EJ Candegraves Harmonic analysis of neural networks Appl Comput Harmon Anal 6 197ndash218 (1999)

[181] EJ Candegraves Ridgelets and the representation of mutilated Sobolev functions SIAM JMath Anal 33 347ndash368 (2001)

[182] EJ Candegraves L Demanet Curvelets and Fourier integral operators CR Acad Sci ParisSeacuter I Math 336 395ndash398 (2003)

[183] EJ Candegraves L Demanet The curvelet representation of wave propagators is optimallysparse Commun Pure Appl Math 58 1472ndash1528 (2004)


[185] EJ Candegraves DL Donoho Curvelets ndash A surprisingly effective nonadaptive representationfor objects with edges in Curves and Surfaces ed by LL Schumaker et al (VanderbiltUniversity Press Nashville TN 1999)

[186] EJ Candegraves DL Donoho Ridgelets A key to higher-dimensional intermittency PhilTrans R Soc Lond A 357 2495ndash2509 (1999)

[187] EJ Candegraves DL Donoho Curvelets multiresolution representation and scaling laws inWavelet Applications in Signal and Image Processing VIII ed by A Aldroubi A LaineM Unser SPIE Proceedings vol 4119 (SPIE Bellingham WA 2000) pp 1ndash12

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[189] EJ Candegraves DL Donoho New tight frames of curvelets and optimal representations ofobjects with piecewise C2 singularities Commun Pure Appl Math 57 219ndash266 (2004)

[190] EJ Candegraves DL Donoho Continuous curvelet transform I Resolution of the wavefrontset II Discretization and frames Appl Comput Harmon Anal 19 162ndash197 198ndash222(2005)

[191] EJ Candegraves F Guo New multiscale transforms minimum total variationsynthesisApplications to edge-preserving image reconstruction Signal Proc 82 1519ndash1543 (2002)

[192] EJ Candegraves L Demanet D Donoho L Ying Fast discrete curvelet transforms MultiscaleModel Simul 5 861ndash899 (2006)

[193] AL Carey Square integrable representations of non-unimodular groups Bull AustrMath Soc 15 1ndash12 (1976)

[194] AL Carey Group representations in reproducing kernel Hilbert spaces Rep Math Phys14 247ndash259 (1978)

[195] P Carruthers MM Nieto Phase and angle variables in quantum mechanics Rev ModPhys 40 411ndash440 (1968)

[196] PG Casazza G Kutyniok Frames of subspaces in Wavelets Frames and Operator The-ory Contemporary Mathematics vol 345 (American Mathematical Society ProvidenceRI 2004) pp 87ndash113

[197] PG Casazza D Han DR Larson Frames for Banach spaces Contemp Math 247 149ndash182 (1999)

[198] P Casazza O Christensen S Li A Lindner Riesz-Fischer sequences and lower framebounds Z Anal Anwend 21 305ndash314 (2002)

[199] PG Casazza G Kutyniok S Li Fusion frames and distributed processing ApplComputHarmon Anal 25 114ndash132 (2008)

[200] DPL Castrigiano RW Henrichs Systems of covariance and subrepresentations ofinduced representations Lett Math Phys 4 169ndash175 (1980)

[201] U Cattaneo Densities of covariant observables J Math Phys 23 659ndash664 (1982)[202] A Cerioni L Genovese I Duchemin Th Deutsch Accurate complex scaling of three

dimensional numerical potentials Preprint (2013) arXiv13036439v2[203] S-J Chang K-J Shi Evolution and exact eigenstates of a resonant quantum system Phys

Rev A 34 7ndash22 (1986)[204] SHH Chowdhury ST Ali All the groups of signal analysis from the (1+1) affine Galilei

group J Math Phys 52 103504 (2011)[205] SL Chown Antarctic marine biodiversity and deep-sea hydrothermal vents PLoS Biol

10 1ndash4 (2012)[206] C Cishahayo S De Biegravevre On the contraction of the discrete series of SU(11) Ann Inst

Fourier (Grenoble) 43 551ndash567 (1993)[207] M Clerc and S Mallat Shape from texture and shading with wavelets in Dynamical

Systems Control Coding Computer Vision Progress in Systems and Control Theory 25393ndash417 (1999)

[208] L Cohen General phase-space distribution functions J Math Phys 7 781ndash786 (1966)[209] A Cohen I Daubechies J-C Feauveau Biorthogonal bases of compactly supported

wavelets Commun Pure Appl Math 45 485ndash560 (1992)[210] R Coifman Y Meyer MV Wickerhauser Wavelet analysis and signal processing

in Wavelets and Their Applications ed by MB Ruskai G Beylkin R CoifmanI Daubechies S Mallat Y Meyer L Raphael (Jones and Bartlett Boston 1992)pp 153ndash178

[211] R Coifman Y Meyer MV Wickerhauser Entropy-based algorithms for best basisselection IEEE Trans Inform Theory 38 713ndash718 (1992)

[212] R Coquereaux A Jadczyk Conformal theories curved spaces relativistic wavelets andthe geometry of complex domains Rev Math Phys 2 1ndash44 (1990)

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[213] A Coron L Vanhamme J-P Antoine P Van Hecke S Van Huffel The filtering approachto solvent peak suppression in MRS A critical review J Magn Reson 152 26ndash40 (2001)

[214] N Cotfas J-P Gazeau Finite tight frames and some applications (topical review) J PhysA Math Theor 43 193001 (2010)

[215] N Cotfas J-P Gazeau K Goacuterska Complex and real Hermite polynomials and relatedquantizations J Phys A Math Theor 43 305304 (2010)

[216] N Cotfas J-P Gazeau A Vourdas Finite-dimensional Hilbert space and frame quantiza-tion J Phys A Math Gen 44 175303 (2011)

[217] EMF Curado MA Rego-Monteiro LMCS Rodrigues Y Hassouni Coherent statesfor a degenerate system The hydrogen atom Physica A 371 16ndash19 (2006)

[218] S Dahlke P Maass The affine uncertainty principle in one and two dimensions CompMath Appl 30 293ndash305 (1995)

[219] S Dahlke W Dahmen E Schmidt I Weinreich Multiresolution analysis and wavelets onS

2 and S3 Numer Funct Anal Optim 16 19ndash41 (1995)

[220] S Dahlke V Lehmann G Teschke Applications of wavelet methods to the analysis ofmeteorological radar data - An overview Arabian J Sci Eng 28 3ndash44 (2003)

[221] S Dahlke G Kutyniok P Maass C Sagiv H-G Stark G Teschke The uncertaintyprinciple associated with the continuous shearlet transform Int J Wavelets MultiresolutInf Process 6 157ndash181 (2008)

[222] S Dahlke G Kutyniok G Steidl G Teschke Shearlet coorbit spaces and associatedBanach frames Appl Comput Harmon Anal 27 195ndash214 (2009)

[223] S Dahlke G Steidl G Teschke The continuous shearlet transform in arbitrary spacedimensions J Fourier Anal Appl 16 340ndash364 (2010)

[224] S Dahlke G Steidl G Teschke Shearlet coorbit spaces Compactly supported analyzingshearlets traces and embeddings J Fourier Anal Appl 17 1232ndash1355 (2011)

[225] T Dallard GR Spedding 2-D wavelet transforms Generalisation of the Hardy space andapplication to experimental studies Eur J Mech BFluids 12 107ndash134 (1993)

[226] C Daskaloyannis Generalized deformed oscillator and nonlinear algebras J Phys AMath Gen 24 L789ndashL794 (1991)

[227] C Daskaloyannis K Ypsilantis A deformed oscillator with Coulomb energy spectrumJ Phys A Math Gen 25 4157ndash4166 (1992)

[228] I Daubechies On the distributions corresponding to bounded operators in the Weylquantization Commun Math Phys 75 229ndash238 (1980)

[229] I Daubechies and A Grossmann An integral transform related to quantization I J MathPhys 21 2080ndash2090 (1980)

[230] I Daubechies A Grossmann J Reignier An integral transform related to quantization IIJ Math Phys 24 239ndash254 (1983)

[231] I Daubechies Orthonormal bases of compactly supported wavelets Commun Pure ApplMath 41 909ndash996 (1988)

[232] I Daubechies The wavelet transform time-frequency localisation and signal analysisIEEE Trans Inform Theory 36 961ndash1005 (1990)

[233] I Daubechies S Maes A nonlinear squeezing of the continuous wavelet transform basedon auditory nerve models in Wavelets in Medicine and Biology ed by A Aldroubi MUnser (CRC Press Boca Raton 1996) pp 527ndash546

[234] I Daubechies A Grossmann Y Meyer Painless nonorthogonal expansions J Math Phys27 1271ndash1283 (1986)

[235] ER Davies Introduction to texture analysis in Handbook of texture analysis ed by MMirmehdi X Xie J Suri (World Scientific Singapore 2008) pp 1ndash31

[236] R De Beer D van Ormondt FTAW Wajer S Cavassila D Graveron-Demilly S VanHuffel SVD-based modelling of medical NMR signals in SVD and Signal ProcessingIII Algorithms Architectures and Applications ed by M Moonen B De Moor (Elsevier(North-Holland) Amsterdam 1995) pp 467ndash474

[237] S De Biegravevre Coherent states over symplectic homogeneous spaces J Math Phys 301401ndash1407 (1989)

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[238] S De Biegravevre JA Gonzalez Semi-classical behaviour of the Weyl correspondence on thecircle in Group-Theoretical Methods in Physics (Proc Salamanca 1992) ed by M delOlmo M Santander J Mateos Guilarte (CIEMAT Madrid 1993) pp 343ndash346

[239] S De Biegravevre JA Gonzaacutelez Semiclassical behaviour of coherent states on the circle inQuantization and Coherent States Methods in Physics ed by A Odzijewicz et al (WorldScientific Singapore 1993)

[240] S De Biegravevre AE Gradechi Quantum mechanics and coherent states on the anti-de Sitterspace-time and their Poincareacute contraction Ann Inst H Poincareacute 57 403ndash428 (1992)

[241] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 23878ndash889 2004ndash2015 (1982)

[242] J Deenen C Quesne Dynamical group of collective states I II III J Math Phys 251638ndash1650 (1984)

[243] J Deenen C Quesne Partially coherent states of the real symplectic group J Math Phys25 2354ndash2366 (1984)

[244] J Deenen C Quesne Boson representations of the real symplectic group and theirapplication to the nuclear collective model J Math Phys 26 2705ndash2716 (1985)

[245] R Delbourgo Minimal uncertainty states for the rotation and allied groups J Phys AMath Gen 10 1837ndash1846 (1977)

[246] R Delbourgo J R Fox Maximum weight vectors possess minimal uncertainty J PhysA Math Gen 10 L233ndashL235 (1977)

[247] V Delouille J de Patoul J-F Hochedez L Jacques J-P Antoine Wavelet spectrumanalysis of EITSoHO images Solar Phys 228 301ndash321 (2005)

[248] N Delprat B Escudieacute P Guillemain R Kronland-Martinet P Tchamitchian B Tor-reacutesani Asymptotic wavelet and Gabor analysis Extraction of instantaneous frequenciesIEEE Trans Inform Theory 38 644ndash664 (1992)

[249] Th Deutsch L Genovese Wavelets for electronic structure calculations Collection SocFr Neut 12 33ndash76 (2011)

[250] B Dewitt Quantum theory of gravity I The canonical theory Phys Rev 160 1113ndash1148(1967)

[251] RH Dicke Coherence in spontaneous radiation processes Phys Rev 93 99ndash110 (1954)[252] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 1

Local intermittency measure in cascade and avalanche scenarios Solar Phys 282 471ndash481(2013)

[253] AN Dinkelaker AL MacKinnon Wavelets intermittency and solar flare hard X-rays 2LIM analysis of high time resolution BATSE data Solar Phys 282 483ndash501 (2013)

[254] MN Do M Vetterli Contourlets in Beyond Wavelets ed by GV Welland (AcademicSan Diego 2003) pp 83ndash105

[255] MN Do M Vetterli The contourlet transform An efficient directional multiresolutionimage representation IEEE Trans Image Process 14 2091ndash2106 (2005)

[256] VV Dodonov Nonclassical states in quantum optics A ldquosqueezedrdquo review of the first 75years J Opt B Quant Semiclass Opot 4 R1ndashR33 (2002)

[257] DL Donoho Nonlinear wavelet methods for recovery of signals densities and spectrafrom indirect and noisy data in Different Perspectives on Wavelets Proceedings ofSymposia in Applied Mathematics vol 38 ed by I Daubechies (American MathematicalSociety Providence RI 1993) pp 173ndash205

[258] DL Donoho Wedgelets Nearly minimax estimation of edges Ann Stat 27 859ndash897(1999)

[259] DL Donoho X Huo Beamlet pyramids A new form of multiresolution analysis suitedfor extracting lines curves and objects from very noisy image data in SPIE Proceedingsvol 5914 (SPIE Bellingham WA 2005) pp 1ndash12

References 557

[260] AH Dooley Contractions of Lie groups and applications to analysis in Topics in ModernHarmonic Analysis vol I (Istituto Nazionale di Alta Matematica Francesco Severi Roma1983) pp 483ndash515

[261] AH Dooley JW Rice Contractions of rotation groups and their representations MathProc Camb Phil Soc 94 509ndash517 (1983)

[262] AH Dooley JW Rice On contractions of semisimple Lie groups Trans Amer MathSoc 289 185ndash202 (1985)

[263] JR Driscoll DM Healy Computing Fourier transforms and convolutions on the 2-sphereAdv Appl Math 15 202ndash250 (1994)

[264] H Drissi F Regragui J-P Antoine M Bennouna Wavelet transform analysis of visualevoked potentials Some preliminary results ITBM-RBM 21 84ndash91 (2000)

[265] RJ Duffin AC Schaeffer A class of nonharmonic Fourier series Trans Amer MathSoc 72 341ndash366 (1952)

[266] M Duflo CC Moore On the regular representation of a nonunimodular locally compactgroup J Funct Anal 21 209ndash243 (1976)

[267] M Duval-Destin R Murenzi Spatio-temporal wavelets Application to the analysis ofmoving patterns in Progress in Wavelet Analysis and Applications (Proc Toulouse 1992)ed by Y Meyer S Roques (Ed Frontiegraveres Gif-sur-Yvette 1993) pp 399ndash408

[268] M Duval-Destin M-A Muschietti B Torreacutesani Continuous wavelet decompositionsmultiresolution and contrast analysis SIAM J Math Anal 24 739ndash755 (1993)

[269] SJL van Eindhoven JLH Meyers New orthogonality relations for the Hermitepolynomials and related Hilbert spaces J Math Anal Appl 146 89ndash98 (1990)

[270] M ElBaz R Fresneda J-P Gazeau Y Hassouni Coherent state quantization of para-grassmann algebras J Phys A Math Theor 43 385202 (2010) Corrigendum J PhysA Math Theor 45 (2012)

[271] A Elkharrat J-P Gazeau F Deacutenoyer Multiresolution of quasicrystal diffraction spectraActa Cryst A65 466ndash489 (2009)

[272] Q Fan Phase space analysis of the identity decompositions J Math Phys 34 3471ndash3477(1993)

[273] M Fanuel S Zonetti Affine quantization and the initial cosmological singularity Euro-phys Lett 101 10001 (2013)

[274] M Farge Wavelet transforms and their applications to turbulence Annu Rev Fluid Mech24 395ndash457 (1992)

[275] M Farge N Kevlahan V Perrier E Goirand Wavelets and turbulence Proc IEEE 84639ndash669 (1996)

[276] M Farge NK-R Kevlahan V Perrier K Schneider Turbulence analysis modellingand computing using wavelets in Wavelets in Physics Chap 4 ed by JC van den Berg(Cambridge University Press Cambridge 1999)

[277] HG Feichtinger Coherent frames and irregular sampling in Recent Advances in FourierAnalysis and Its applications ed by JS Byrnes JL Byrnes (Kluwer Dordrecht 1990)pp 427ndash440

[278] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions I J Funct Anal 86 307ndash340 (1989)

[279] HG Feichtinger KH Groumlchenig Banach spaces related to integrable group representa-tions and their atomic decompositions II Mh Math 108 129ndash148 (1989)

[280] M Flensted-Jensen Discrete series for semisimple symmetric spaces Ann of Math 111253ndash311 (1980)

[281] K Flornes A Grossmann M Holschneider B Torreacutesani Wavelets on discrete fieldsAppl Comput Harmon Anal 1 137ndash146 (1994)

[282] V Fock Zur Theorie der Wasserstoffatoms Zs f Physik 98 145ndash54 (1936)[283] M Fornasier H Rauhut Continuous frames function spaces and the discretization

problem J Fourier Anal Appl 11 245ndash287 (2005)

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[284] W Freeden M Schreiner Orthogonal and non-orthogonal multiresolution analysis scalediscrete and exact fully discrete wavelet transform on the sphere Constr Approx 14 493ndash515 (1997)

[285] W Freeden U Windheuser Combined spherical harmonic and wavelet expansion mdash Afuture concept in Earthrsquos gravitational determination Appl Comput Harmon Anal 4 1ndash37 (1997)

[286] W Freeden T Maier S Zimmermann A survey on wavelet methods for (geo)applicationsRevista Mathematica Complutense 16 (2003) 277ndash310

[287] W Freeden M Schreiner Biorthogonal locally supported wavelets on the sphere based onzonal kernel functions J Fourier Anal Appl 13 693ndash709 (2007)

[288] WT Freeman EH Adelson The design and use of steerable filters IEEE Trans PatternAnal Machine Intell 13 891ndash906 (1991)

[289] L Freidel ER Livine U(N) coherent states for loop quantum gravity J Math Phys 52052502 (2011)

[290] J Froment S Mallat Arbitrary low bit rate image compression using wavelets in Progressin Wavelet Analysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques(Ed Frontiegraveres Gif-sur-Yvette 1993) pp 413ndash418 and references therein

[291] L Freidel S Speziale Twisted geometries A geometric parameterisation of SU(2) phasespace Phys Rev D 82 084040 (2010)

[292] H Fuumlhr Wavelet frames and admissibility in higher dimensions J Math Phys 37 6353ndash6366 (1996)

[293] H Fuumlhr M Mayer Continuous wavelet transforms from semidirect products Cyclicrepresentations and Plancherel measure J Fourier Anal Appl 8 375ndash396 (2002)

[294] D Gabor Theory of communication J Inst Electr Engrg(London) 93 429ndash457 (1946)[295] J-P Gabardo D Han Frames associated with measurable spaces Adv Comput Math 18

127ndash147 (2003)[296] E Galapon Paulirsquos theorem and quantum canonical pairs The consistency of a bounded

self-adjoint time operator canonically conjugate to a Hamiltonian with non-empty pointspectrum Proc R Soc Lond A 458 451ndash472 (2002)

[297] PL Garciacutea de Leacuteon J-P Gazeau Coherent state quantization and phase operator PhysLett A 361 301ndash304 (2007)

[298] L Garciacutea de Leoacuten J-P Gazeau J Queacuteva The infinite well revisited Coherent states andquantization Phys Lett A 372 3597ndash3607 (2008)

[299] T Garidi J-P Gazeau E Huguet M Lachiegraveze Rey J Renaud Fuzzy spheres frominequivalent coherent states quantization J Phys A Math Theor 40 10225ndash10249 (2007)

[300] J-P Gazeau Four Euclidean conformal group in atomic calculations Exact analyticalexpressions for the bound-bound two-photon transition matrix elements in the H atomJ Math Phys 19 1041ndash1048 (1978)

[301] J-P Gazeau On the four Euclidean conformal group structure of the sturmian operatorLett Math Phys 3 285ndash292 (1979)

[302] J-P Gazeau Technique Sturmienne pour le spectre discret de lrsquoeacutequation de SchroumldingerJ Phys A Math Gen 13 3605ndash3617 (1980)

[303] J-P Gazeau Four Euclidean conformal group approach to the multiphoton processes in theH atom J Math Phys 23 156ndash164 (1982)

[304] J-P Gazeau A remarkable duality in one particle quantum mechanics between someconfining potentials and (R+Linfin

ε ) potentials Phys Lett 75A 159ndash163 (1980)[305] J-P Gazeau SL(2R)-coherent states and integrable systems in classical and quantum

physics in Quantization Coherent States and Complex Structures ed by J-P AntoineST Ali W Lisiecki IM Mladenov A Odzijewicz (Plenum Press New York and London1995) pp 147ndash158

[306] J-P Gazeau S Graffi Quantum harmonic oscillator A relativistic and statistical point ofview Boll Unione Mat Ital 11-A 815ndash839 (1997)

[307] J-P Gazeau V Hussin Poincareacute contraction of SU(11) Fock-Bargmann structure J PhysA Math Gen 25 1549ndash1573 (1992)

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[308] J-P Gazeau R Kanamoto Action-angle coherent states and related quantization inProceedings of QTS7 Colloquium Prague 2011 Journal of Physics Conference Seriesvol 343 (2012) p 012038-1-9

[309] J-P Gazeau JR Klauder Coherent states for systems with discrete and continuousspectrum J Phys A Math Gen 32 123ndash132 (1999)

[310] J-P Gazeau P Monceau Generalized coherent states for arbitrary quantum systems inColloquium M Flato (Dijon Sept 99) vol II (Kluumlwer Dordrecht 2000) pp 131ndash144

[311] J-P Gazeau M Novello The question of mass in (Anti-) de Sitter space-times J Phys AMath Theor 41 304008 (2008)

[312] J-P Gazeau M del Olmo q-coherent states quantization of the harmonic oscillator AnnPhys (NY) 330 220ndash245 (2013) arXiv12071200 [quant-ph]

[313] J-P Gazeau J Patera Tau-wavelets of Haar J Phys A Math Gen 29 4549ndash4559 (1996)[314] J-P Gazeau W Piechocki Coherent states quantization of a particle in de Sitter space

J Phys A Math Gen 37 6977ndash6986 (2004)[315] J-P Gazeau J Renaud Lie algorithm for an interacting SU(11) elementary system and its

contraction Ann Phys (NY) 222 89ndash121 (1993)[316] J-P Gazeau J Renaud Relativistic harmonic oscillator and space curvature Phys Lett A

179 67ndash71 (1993)[317] J-P Gazeau V Spiridonov Toward discrete wavelets with irrational scaling factor J Math

Phys 37 3001ndash3013 (1996)[318] J-P Gazeau FH Szafraniec Holomorphic Hermite polynomials and non-commutative

plane J Phys A Math Theor 44 495201 (2011)[319] J-P Gazeau J Patera E Pelantovaacute Tau-wavelets in the plane J Math Phys 39 4201ndash

4212 (1998)[320] J-P Gazeau M Andrle C Burdiacutek R Krejcar Wavelet multiresolutions for the Fibonacci

chain J Phys A Math Gen 33 L47ndashL51 (2000)[321] J-P Gazeau M Andrle C Burdiacutek Bernuau spline wavelets and sturmian sequences

J Fourier Anal Appl 10 269ndash300 (2004)[322] J-P Gazeau F-X Josse-Michaux P Monceau Finite dimensional quantizations of the

(q p) plane new space and momentum inequalities Int J Modern Phys B 20 1778ndash1791 (2006)

[323] J-P Gazeau J Mourad J Queacuteva Fuzzy de Sitter space-times via coherent statesquantization in Proceedings of the XXVIth Colloquium on Group Theoretical Methodsin Physics New York 2006 ed by J Birman S Catto B Nicolescu (Canopus PublishingLimited London 2009)

[324] D Geller A Mayeli Continuous wavelets on compact manifolds Math Z 262 895ndash927(2009)

[325] D Geller A Mayeli Nearly tight frames and space-frequency analysis on compactmanifolds Math Z 263 235ndash264 (2009)

[326] L Genovese B Videau M Ospici Th Deutsch S Goedecker J-F Mhaut Daubechieswavelets for high performance electronic structure calculations The BigDFT project CR Mecanique 339 149ndash164 (2011)

[327] G Gentili C Stoppato Power series and analyticity over the quaternions Math Ann 352113ndash131 (2012)

[328] G Gentili DC Struppa A new theory of regular functions of a quaternionic variable AdvMath 216 279ndash301 (2007)

[329] C Geyer K Daniilidis Catadioptric projective geometry Int J Comput Vision 45 223ndash243 (2001)

[330] R Gilmore Geometry of symmetrized states Ann Phys (NY) 74 391ndash463 (1972)[331] R Gilmore On properties of coherent states Rev Mex Fis 23 143ndash187 (1974)[332] J Ginibre Statistical ensembles of complex quaternion and real matrices J Math Phys

6 440ndash449 (1965)[333] RJ Glauber The quantum theory of optical coherence Phys Rev 130 2529ndash2539 (1963)

560 References

[334] RJ Glauber Coherent and incoherent states of radiation field Phys Rev 131 2766ndash2788(1963)

[335] J Glimm Locally compact transformation groups Trans Amer Math Soc 101 124ndash138(1961)

[336] R Godement Sur les relations drsquoorthogonaliteacute de V Bargmann C R Acad Sci Paris 255521ndash523 657ndash659 (1947)

[337] C Gonnet B Torreacutesani Local frequency analysis with two-dimensional wavelet trans-form Signal Proc 37 389ndash404 (1994)

[338] JA Gonzalez MA del Olmo Coherent states on the circle J Phys A Math Gen 318841ndash8857 (1998)

[339] XGonze B Amadon et al ABINIT First-principles approach to material and nanosystemproperties Computer Physics Comm 180 2582ndash2615 (2009)

[340] KM Gograverski E Hivon AJ Banday BD Wandelt FK Hansen M Reinecke MBartelmann HEALPix A framework for high-resolution discretization and fast analysisof data distributed on the sphere Astrophys J 622 759ndash771 (2005)

[341] P Goupillaud A Grossmann J Morlet Cycle-octave and related transforms in seismicsignal analysis Geoexploration 23 85ndash102 (1984)

[342] KH Groumlchenig A new approach to irregular sampling of band-limited functions in RecentAdvances in Fourier Analysis and Its applications ed by JS Byrnes JL Byrnes (KluwerDordrecht 1990) pp 251ndash260

[343] KH Groumlchenig Gabor analysis over LCA groups in Gabor Analysis and Algorithms ndashTheory and Applications ed by HG Feichtinger T Strohmer (Birkhaumluser Boston-Basel-Berlin 1998) pp 211ndash231

[344] HJ Groenewold On the principles of elementary quantum mechanics Physica 12 405ndash460 (1946)

[345] P Grohs Continuous shearlet tight frames J Fourier Anal Appl 17 506ndash518 (2011)[346] P Grohs G Kutyniok Parabolic molecules preprint TU Berlin (2012)[347] M Grosser A note on distribution spaces on manifolds Novi Sad J Math 38 121ndash128

(2008)[348] A Grossmann Parity operator and quantization of δ -functions Commun Math Phys 48

191ndash194 (1976)[349] A Grossmann J Morlet Decomposition of Hardy functions into square integrable

wavelets of constant shape SIAM J Math Anal 15 723ndash736 (1984)[350] A Grossmann J Morlet Decomposition of functions into wavelets of constant shape and

related transforms in Mathematics + Physics Lectures on recent results I ed by L Streit(World Scientific Singapore 1985) pp 135ndash166

[351] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations I General results J Math Phys 26 2473ndash2479 (1985)

[352] A Grossmann J Morlet T Paul Integral transforms associated to square integrablerepresentations II Examples Ann Inst H Poincareacute 45 293ndash309 (1986)

[353] A Grossmann R Kronland-Martinet J Morlet Reading and understanding the contin-uous wavelet transform in Wavelets Time-Frequency Methods and Phase Space (ProcMarseille 1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (SpringerBerlin 1990) pp 2ndash20

[354] P Guillemain R Kronland-Martinet B Martens Estimation of spectral lines with helpof the wavelet transform Application in NMR spectroscopy in Wavelets and Applications(Proc Marseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp38ndash60

[355] H de Guise M Bertola Coherent state realizations of su(n+ 1) on the n-torus J MathPhys 43 3425ndash3444 (2002)

[356] K Guo D Labate Representation of Fourier Integral Operators using shearlets J FourierAnal Appl 14 327ndash371 (2008)

References 561

[357] K Guo G Kutyniok D Labate Sparse multidimensional representations usinganisotropic dilation and shear operators in Wavelets and Spines (Athens GA 2005)(Nashboro Press Nashville TN 2006) pp 189ndash201

[358] K Guo D Labate W-Q Lim G Weiss E Wilson Wavelets with composite dilationsand their MRA properties Appl Comput Harmon Anal 20 202ndash236 (2006)

[359] EA Gutkin Overcomplete subspace systems and operator symbols Funct Anal Appl 9260ndash261 (1975)

[360] G Gyoumlrgyi Integration of the dynamical symmetry groups for the 1r potential Acta PhysAcad Sci Hung 27 435ndash439 (1969)

[361] BC Hall The Segal-Bargmann ldquoCoherent Staterdquo transform for compact Lie groups JFunct Analysis 122 103ndash151 (1994)

[362] B Hall JJ Mitchell Coherent states on spheres J Math Phys 43 1211ndash1236 (2002)[363] DK Hammond P Vandergheynst R Gribonval Wavelets on graphs via spectral theory

Appl Comput Harmon Anal 30 129ndash150 (2011)[364] Y Hassouni EMF Curado MA Rego-Monteiro Construction of coherent states for

physical algebraic system Phys Rev A 71 022104 (2005)[365] J He H Liu Admissible wavelets associated with the affine automorphism group of the

Siegel upper half-plane J Math Anal Appl 208 58ndash70 (1997)[366] J He H Liu Admissible wavelets associated with the classical domain of type one

Approx Appl 14 (1998) 89ndash105[367] J He L Peng Wavelet transform on the symmetric matrix space preprint Beijing (1997)

(unpublished)[368] J He L Peng Admissible wavelets on the unit disk Complex Variables 35 109ndash119

(1998)[369] DM Healy Jr FE Schroeck Jr On informational completeness of covariant localization

observables and Wigner coefficients J Math Phys 36 453ndash507 (1995)[370] C Heil D Walnut Continuous and discrete wavelet transforms SIAM Review 31 628ndash

666 (1989)[371] K Hepp EH Lieb On the superradiant phase transition for molecules in a quantized

radiation field The Dicke maser model Ann Phys (NY) 76 360ndash404 (1973)[372] K Hepp EH Lieb Equilibrium statistical mechanics of matter interacting with the

quantized radiation field Phys Rev A 8 2517ndash2525 (1973)[373] JA Hogan JD Lakey Extensions of the Heisenberg group by dilations and frames Appl

Comput Harmon Anal 2 174ndash199 (1995)[374] AL Hohoueacuteto K Thirulogasanthar ST Ali J-P Antoine Coherent states lattices and

square integrability of representations J Phys A Math Gen36 11817ndash11835 (2003)[375] M Holschneider On the wavelet transformation of fractal objects J Stat Phys 50 963ndash

993 (1988)[376] M Holschneider Wavelet analysis on the circle J Math Phys 31 39ndash44 (1990)[377] M Holschneider Inverse Radon transforms through inverse wavelet transforms Inv Probl

7 853ndash861 (1991)[378] M Holschneider Localization properties of wavelet transforms J Math Phys 34 3227ndash

3244 (1993)[379] M Holschneider General inversion formulas for wavelet transforms J Math Phys 34

4190ndash4198 (1993)[380] M Holschneider Wavelet analysis over abelian groups Applied Comput Harmon Anal

2 52ndash60 (1995)[381] M Holschneider Continuous wavelet transforms on the sphere J Math Phys 37 4156ndash

4165 (1996)[382] M Holschneider I Iglewska-Nowak Poisson wavelets on the sphere J Fourier Anal

Appl 13 405ndash419 (2007)

562 References

[383] M Holschneider R Kronland-Martinet J Morlet P Tchamitchian A real-time algorithmfor signal analysis with the help of wavelet transform in Wavelets Time-FrequencyMethods and Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 286ndash297

[384] M Holschneider P Tchamitchian Pointwise analysis of Riemannrsquos ldquonondifferentiablerdquofunction Invent Math 105 157ndash175 (1991)

[385] GR Honarasa MK Tavassoly M Hatami R Roknizadeh Nonclassical properties ofcoherent states and excited coherent states for continuous spectra J Phys A Math Theor44 085303 (2011)

[386] M Hongoh Coherent states associated with the continuous spectrum of noncompactgroups J Math Phys 18 2081ndash2085 (1977)

[387] A Horzela FH Szafraniec A measure free approach to coherent states J Phys A MathGen 45 244018 (2012)

[388] W-L Hwang S Mallat Characterization of self-similar multifractals with waveletmaxima Appl Comput Harmon Anal 1 316ndash328 (1994)

[389] W-L Hwang C-S Lu P-C Chung Shape from texture Estimation of planar surfaceorientation through the ridge surfaces of continuous wavelet transform IEEE Trans ImageProc 7 773ndash780 (1998)

[390] I Iglewska-Nowak M Holschneider Frames of Poisson wavelets on the sphere ApplComput Harmon Anal 28 227ndash248 (2010)

[391] E Inoumlnuuml EP Wigner On the contraction of groups and their representations Proc NatAcad Sci U S 39 510ndash524 (1953)

[392] S Iqbal F Saif Generalized coherent states and their statistical characteristics in power-law potentials J Math Phys 52 082105 (2011)

[393] CJ Isham JR Klauder Coherent states for n-dimensional Euclidean groups E(n) andtheir application J MathPhys 32 607ndash620 (1991)

[394] L Jacques J-P Antoine Multiselective pyramidal decomposition of images Wavelets withadaptive angular selectivity Int J Wavelets Multires Inform Proc 5 785ndash814 (2007)

[395] L Jacques L Duval C Chaux G Peyreacute A panorama on multiscale geometric rep-resentations intertwining spatial directional and frequency selectivity Signal Proc 912699ndash2730 (2011)

[396] HR Jalali M K Tavassoly On the ladder operators and nonclassicality of generalizedcoherent state associated with a particle in an infinite square well preprint (2013)arXiv13034100v1 [quant-ph]

[397] C Johnston On the pseudo-dilation representations of Flornes Grossmann Holschneiderand Torreacutesani Appl Comput Harmon Anal 3 377ndash385 (1997)

[398] G Kaiser Phase-space approach to relativistic quantum mechanics I Coherent staterepresentation for massive scalar particles J MathPhys 18 952ndash959 (1977)

[399] G Kaiser Phase-space approach to relativistic quantum mechanics II Geometrical aspectsJ MathPhys 19 502ndash507 (1978)

[400] C Kalisa B Torreacutesani N-dimensional affine Weyl-Heisenberg wavelets Ann Inst HPoincareacute 59 201ndash236 (1993)

[401] W Kaminski J Lewandowski T Pawłowski Quantum constraints Dirac observables andevolution group averaging versus the Schroumldinger picture in LQC Class Quant Grav 26245016 (2009)

[402] MR Karim ST Ali A relativistic windowed Fourier transform preprint ConcordiaUniversity Montreacuteal (1997) (unpublished)

[403] M R Karim ST Ali M Bodruzzaman A relativistic windowed Fourier transform inProceedings of IEEE SoutheastCon 2000 Nashville Tennessee pp 253ndash260 (2000)

[404] T Kawazoe Wavelet transforms associated to a principal series representation of semisim-ple Lie groups I II Proc Japan Acad Ser A ndash Math Sci 71 154ndash157 158ndash160 (1995)

[405] T Kawazoe Wavelet transform associated to an induced representation of SL(n+ 2R)Ann Inst H Poincareacute 65 1ndash13 (1996)

References 563

[406] P Kittipoom G Kutyniok W-Q Lim Irregular shearlet frames Geometry and approxi-mation properties J Fourier Anal Appl 17 604ndash639 (2011)

[407] P Kittipoom G Kutyniok W-Q Lim Construction of compactly supported shearletframes Constr Approx 35 21ndash72 (2012)

[408] J Kiukas P Lahti K Ylinenc Phase space quantization and the operator moment problemJ Math Phys 47 072104 (2006)

[409] JR Klauder Continuous-representation theory I Postulates of continuous-representationtheory J Math Phys 4 1055ndash1058 (1963)

[410] JR Klauder Continuous-representation theory II Generalized relation between quantumand classical dynamics J Math Phys 4 1058ndash1073 (1963)

[411] JR Klauder Path integrals for affine variables in Functional Integration Theory andApplications ed by J-P Antoine E Tirapegui (Plenum Press New York and London1980) pp 101ndash119

[412] JR Klauder Are coherent states the natural language of quantum mechanics inFundamental Aspects of Quantum Theory ed by V Gorini A Frigerio NATO ASI Seriesvol B 144 (Plenum Press New York 1986) pp 1ndash12

[413] JR Klauder Quantization without quantization Ann Phys (NY) 237 147ndash160 (1995)[414] JR Klauder Coherent states for the hydrogen atom J Phys A Math Gen 29 L293ndash

L296 (1996)[415] JR Klauder An affinity for affine quantum gravity Proc Steklov Inst Math 272 169ndash176

(2011) and references therein[416] JR Klauder RF Streater A wavelet transform for the Poincareacute group J Math Phys 32

1609ndash1611 (1991)[417] JR Klauder RF Streater Wavelets and the Poincareacute half-plane J Math Phys 35 471ndash

478 (1994)[418] JR Klauder K Penson J-M Sixdeniers Constructing coherent states through solutions

of Stieltjes and Hausdorff moment problems Phys Rev A 64 013817 (2001)[419] A Kleppner RL Lipsman The Plancherel formula for group extensions Ann Ec Norm

Sup 5 459ndash516 (1972)[420] AB Klimov C Muntildeoz Coherent isotropic and squeezed states in a N-qubit system Phys

Scr 87 038110 (2013)[421] A Klyashko Dynamical symmetry approach to entanglement in Physics and Theoretical

Computer Science From Numbers and Languages to (Quantum) Cryptography - NATOSecurity through Science Series D - Information and Communication Security vol 7 edby J-P Gazeau J Nesetril B Rovan (IOS Press Washington DC 2007) pp 25ndash54

[422] S Kobayashi Irreducibility of certain unitary representations J Math Soc Japan 20 638ndash642 (1968)

[423] K Kowalski J Rembielinski LC Papaloucas Coherent states for a quantum particle ona circle J Phys A Math Gen 29 4149ndash4167 (1996)

[424] K Kowalski J Rembielinski Quantum mechanics on a sphere and coherent states J PhysA Math Gen 33 6035ndash6048 (2000)

[425] K Kowalski J Rembielinski The Bargmann representation for the quantum mechanicson a sphere J Math Phys 42 4138ndash4147 (2001)

[426] C Kristjansen J Plefka GW Semenoff M Staudacher A new double-scaling limit ofN = 4 super-Yang-Mills theory and pp-wave strings Nuclear Phys B 643 3ndash30 (2002)

[427] M Kulesh M Holschneider MS Diallo Geophysical wavelet library Applications ofthe continuous wavelet transform to the polarization and dispersion analysis of signalsComput Geosci 34 1732ndash1752 (2008)

[428] R Kunze On the Frobenius reciprocity theorem for square integrable representationsPacific J Math 53 465ndash471 (1974)

[429] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal I J Magn Reson 84 604ndash610 (1989)

564 References

[430] Y Kuroda A Wada T Yamazaki K Nagayama Postacquisition data processing methodfor suppression of the solvent signal II The weighted first derivative J Magn Reson 88141ndash145 (1990)

[431] G Kutyniok D Labate Resolution of the wavefront set using continuous shearlets TransAmer Math Soc 361 2719ndash2754 (2009)

[432] G Kutyniok W-Q Lim Compactly supported shearlets are optimally sparse J ApproxTheory 163 1564ndash1589 (2011)

[433] D Labate W-Q Lim G Kutyniok G Weiss Sparse multidimensional representationusing shearlets in Wavelets XI (San Diego CA 2005) ed by M Papadakis A Laine MUnser SPIE Proceedings vol 5914 (SPIE Bellingham WA 2005) pp 254ndash262

[434] P Lahti J-P Pellonpaumlauml Continuous variable tomographic measurements Phys Lett A373 3435ndash3438 (2009)

[435] Lambertrsquos projection see WikipediahttpenwikipediaorgwikiLambert_azimuthal_equal-area_projection

[436] J-P Leduc F Mujica R Murenzi MJT Smith Missile-tracking algorithm using target-adapted spatio-temporal wavelets in Automatic Object Recognition VII SPIE Proceedingsvol 5914 (SPIE Bellingham WA 1997) pp 400ndash411

[437] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal wavelet transforms formotion tracking in IEEE ICASSP 1997 vol 4 (1997) pp 3013ndash3016

[438] J-P Leduc F Mujica R Murenzi MJT Smith Spatio-temporal continuous waveletsapplied to missile warhead detection and tracking in SPIE VCIP rsquo97 vol 3024 ed byJ Biemond EJ Delp (1997) pp 787ndash798

[439] B Leistedt JD McEwen Exact wavelets on the ball IEEE Trans Signal Proc 60 1564ndash1589 (2012)

[440] PG Lemarieacute Y Meyer Ondelettes et bases hilbertiennes Rev Math Iberoamer 2 1ndash18(1986)

[441] C Lemke A Schuck Jr J-P Antoine D Sima Metabolite-sensitive analysis of magneticresonance spectroscopic signals using the continuous wavelet transform Meas SciTechnol 22 (2011) Art 114013

[442] J-M Leacutevy-Leblond Galilei group and non-relativistic quantum mechanics J Math Phys4 776-788 (1963)

[443] J-M Leacutevy-Leblond Galilei group and Galilean invariance in Group Theory and ItsApplications vol II ed by EM Loebl (Academic New York 1971) pp 221ndash299

[444] J-M Leacutevy-Leblond On the conceptual nature of the physical constants Riv Nuovo Cim7 187ndash214 (1977)

[445] EH Lieb The classical limit of quantum spin systems Commun Math Phys 31 327ndash340(1973)

[446] G Lindblad B Nagel Continuous bases for unitary irreducible representations of SU(11)Ann Inst H Poincareacute 13 27ndash56 (1970)

[447] W Lisiecki Kaumlhler coherent states orbits for representations of semisimple Lie groupsAnn Inst H Poincareacute 53 857ndash890 (1990)

[448] A Lisowska Moment-based fast wedgelet transform J Math Imaging Vis 39 180ndash192(2011)

[449] H Liu L Peng Admissible wavelets associated with the Heisenberg group Pacific JMath 180 101ndash123 (1997)

[450] E Livine S Speziale Physical boundary state for the quantum tetrahedron Class QuantGrav 25 085003 (2008)

[451] F Low Complete sets of wave packets in A Passion for Physics ndash Essay in Honor ofGeoffrey Chew ed by C DeTar (World Scientific Singapore 1985) pp 17ndash22

[452] G Mack All unitary ray representations of the conformal group SU(22) with positiveenergy Commun Math Phys 55 1ndash28 (1977)

[453] GW Mackey Imprimitivity for representations of locally compact groups I Proc NatAcad Sci 35 537ndash545 (1949)

References 565

[454] S Majid M Rodriguez-Plaza Random walk and the heat equation on superspace andanyspace J Math Phys 35 3753ndash3760 (1994)

[455] M Mallalieu CR Stroud Jr Rydberg wave packets fractional revivals and classicalorbits in Coherent States Past Present and Future (Proc Oak Ridge 1993) ed by DHFeng JR Klauder M Strayer (World Scientific Singapore 1994) pp 301ndash314

[456] SG Mallat Multifrequency channel decompositions of images and wavelet models IEEETrans Acoust Speech Signal Proc 37 2091ndash2110 (1989)

[457] SG Mallat A theory for multiresolution signal decomposition The wavelet representa-tion IEEE Trans Pattern Anal Machine Intell 11 674ndash693 (1989)

[458] S Mallat W-L Hwang Singularity detection and processing with wavelets IEEE TransInform Theory 38 617ndash643 (1992)

[459] S Mallat Z Zhang Matching pursuits with time frequency dictionaries IEEE TransSignal Proc 41 3397ndash3415 (1993)

[460] S Mallat S Zhong Wavelet maxima representation in Wavelets and Applications (ProcMarseille 1989) ed by Y Meyer (Masson and Springer Paris and Berlin 1991) pp 207ndash284

[461] VI Manrsquoko G Marmo ECG Sudarshan F Zaccaria f -oscillators and non-linearcoherent states Phys Scr 55 528ndash541 (1997)

[462] D Marinucci D Pietrobon A Baldi P Baldi P Cabella G Kerkyacharian P Natoli DPicard N Vittorio Spherical needlets for CMB data analysis Mon Not R Astron Soc383 539ndash545 (2008)

[463] D Marion M Ikura A Bax Improved solvent suppression in one- and two-dimensionalNMR spectra by convolution of time-domain data J Magn Reson 84 425ndash430 (1989)

[464] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs SeacuteminaireBourbaki 662 (1985ndash1986)

[465] Y Meyer Principe drsquoincertitude bases hilbertiennes et algegravebres drsquoopeacuterateurs Asteacuterisque145ndash146 209ndash223 (1987)

[466] Y Meyer H Xu Wavelet analysis and chirps Appl Comput Harmon Anal 4 366ndash379(1997)

[467] L Michel Invariance in quantum mechanics and group extensions in Group TheoreticalConcepts and Methods in Elementary Particle Physics ed by F Guumlrsey (Gordon andBreach New York and London 1964) pp 135ndash200

[468] J Mickelsson J Niederle Contractions of representations of the de Sitter groupsCommun Math Phys 27 167ndash180 (1972)

[469] MM Miller Convergence of the Sudarshan expansion for the diagonal coherent-stateweight functional J Math Phys 9 1270ndash1274 (1968)

[470] V F Molchanov Harmonic analysis on homogeneous spaces in Representation Theoryand Noncommutative Harmonic Analysis II ed by AA Kirillov (Springer Berlin 1995)

[471] MI Monastyrsky AM Perelomov Coherent states and symmetric spaces II Ann InstH Poincareacute 23 23ndash48 (1975)

[472] B Moran S Howard D Cochran Positive-operator-valued measures A general settingfor frames in Excursions in Harmonic Analysis vol 1 2 ed by TD Andrews R BalanJJ Benedetto W Czaja KA Okoudjou (Birkhaumluser Boston 2013) pp 49ndash64

[473] H Moscovici Coherent states representations of nilpotent Lie groups Commun MathPhys 54 63ndash68 (1977)

[474] H Moscovici A Verona Coherent states and square integrable representations Ann InstH Poincareacute 29 139ndash156 (1978)

[475] F Mujica R Murenzi MJT Smith J-P Leduc Robust tracking in compressed imagesequences J Electr Imaging 7 746ndash754 (1998)

[476] R Murenzi Wavelet transforms associated to the n-dimensional Euclidean group withdilations Signals in more than one dimension in Wavelets Time-Frequency Methodsand Phase Space (Proc Marseille 1987) ed by J-M Combes A Grossmann PTchamitchian 2nd edn (Springer Berlin 1990) pp 239ndash246

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[477] MA Muschietti B Torreacutesani Pyramidal algorithms for LittlewoodndashPaley decomposi-tions SIAM J Math Anal 26 925ndash943 (1995)

[478] B Nagel Generalized eigenvectors in group representations in Studies in MathematicalPhysics (Proc Istanbul 1970) ed by AO Barut (Reidel Dordrecht and Boston 1970)pp 135ndash154

[479] MA Naımark Dokl Akad Nauk SSSR 41 359ndash361 (1943) see also B Sz-NagyExtensions of linear transformations in Hilbert space which extend beyond this spaceAppendix to F Riesz B Sz-Nagy Functional Analysis (Frederick Ungar New York 1960)

[480] FJ Narcowich P Petrushev JD Ward Localized tight frames on spheres SIAM J MathAnal 38 574ndash594 (2006)

[481] M Nauenberg Quantum wave packets on Kepler elliptic orbits Phys Rev A 40 1133ndash1136 (1989)

[482] M Nauenberg C Stroud J Yeazell The classical limit of an atom Scient Amer 27024ndash29 (1994)

[483] H Neumann Transformation properties of observables Helv Phys Acta 45 811ndash819(1972)

[484] U Niederer The maximal kinematical invariance group of the free Schroumldinger equationHelv Phys Acta 45 802ndash881 (1972)

[485] MM Nieto LM Simmons Jr Coherent states for general potentials I Formalism IIConfining one-dimensional examples III Nonconfining one-dimensional examples PhysRev D 20 1321ndash1331 1332ndash1341 1342ndash1350 (1979)

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[499] T Paul Affine coherent states and the radial Schroumldinger equation I preprint CPT-84P1710 (1984) (unpublished)

References 567

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[537] D Rosca G Plonka Uniform spherical grids via area preserving projection from the cubeto the sphere J Comput Appl Math 236 1033ndash1041 (2011)

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[540] DJ Rotenberg Application of Sturmian functions to the Schroedinger three-body prob-lem Elastic e+ndashH scattering Ann Phys (NY) 19 262ndash278 (1962)

[541] C Rovelli Zakopane lectures on loop gravity in Proceedings of 3rd Quantum Gravityand Quantum Geometry School 28 Febndash13 March 2011 (Zakopane Poland 2011)arXiv11023660v5

[542] C Rovelli S Speziale A semiclassical tetrahedron Class Quant Grav 23 5861ndash5870(2006)

[543] DJ Rowe Coherent state theory of the noncompact symplectic group J Math Phys 252662ndash2271 (1984)

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[545] DJ Rowe Vector coherent state representations and their inner products J Phys A MathGen 45 244003 (2012) (This paper belongs to the special issue [38])

[546] DJ Rowe J Repka Vector-coherent-state theory as a theory of induced representationsJ Math Phys 32 2614ndash2634 (1991)

[547] DJ Rowe G Rosensteel R Gilmore Vector coherent state representation theory J MathPhys 26 2787ndash2791 (1985)

[548] A Royer Phase states and phase operators for the quantum harmonic oscillator Phys RevA 53 70ndash108 (1996)

[549] J Saletan Contraction of Lie groups J Math Phys 2 1ndash21 (1961)[550] G Saracco A Grossmann P Tchamitchian Use of wavelet transforms in the study of

propagation of transient acoustic signals across a plane interface between two homoge-neous media in Wavelets Time-Frequency Methods and Phase Space (Proc Marseille1987) ed by J-M Combes A Grossmann P Tchamitchian 2nd edn (Springer Berlin1990) pp 139ndash146

[551] P Schroumlder W Sweldens Spherical wavelets Efficiently representing functions on thesphere in Computer Graphics Proceedings (SIGGRAPH95) (ACM Siggraph Los Angeles1995) pp 161ndash175

References 569

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[553] S Scodeller Oslash Rudjord FK Hansen D Marinucci D Geller A Mayeli IntroducingMexican needlets for CMB analysis Issues for practical applications and comparison withstandard needlets Astrophys J 733 (2011) Art 121

[554] H Scutaru Coherent states and induced representations Lett Math Phys 2 101ndash107(1977)

[555] B Simon Distributions and their Hermite expansions J Math Phys 12 140ndash148 (1971)[556] B Simon The classical moment problem as a self-adjoint finite difference operator Adv

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R61ndashR75 (2000)[559] E Slezak A Bijaoui G Mars Identification of structures from galaxy counts Use of the

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[562] SB Sontz Paragrassmann algebras as quantum spaces Part II Toeplitz operators J OperTh (2013 to appear) arXiv12055493

[563] SB Sontz A reproducing kernel and Toeplitz operators in the quantum plane Preprint(2013) arXiv13056986 [math-ph]

[564] SB Sontz Toeplitz quantization of an algebra with conjugation Preprint (2013)arXiv13085454 [math-ph]

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[566] J-L Starck EJ Candegraves DL Donoho The curvelet transform for image denoising IEEETrans Image Proc 11 670ndash684 (2002)

[567] J-L Starck DL Donoho E J Candegraves Astronomical image representation by the curvelettransform Astron Astroph 398 785ndash800 (2003)

[568] J-L Starck Y Moudden P Abrial M Nguyen Wavelets ridgelets and curvelets on thesphere Astron Astroph 446 1191ndash1204 (2006)

[569] MB Stenzel The Segal-Bargmann transform on a symmetric space of compact type JFunct Analysis 165 44ndash58 (1994)

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[571] A Suvichakorn H Ratiney A Bucur S Cavassila J-P Antoine Toward a quantitativeanalysis of in vivo magnetic resonance proton spectroscopic signals using the continuousMorlet wavelet transform Meas Sci Technol 20 (2009) Art 104029

[572] W Sweldens The lifting scheme A custom-design construction of biorthogonal waveletsApplied Comput Harmon Anal 3 1186ndash1200 (1996)

[573] W Sweldens The lifting scheme A construction of second generation wavelets SIAM JMath Anal 29 511ndash546 (1998)

[574] FH Szafraniec The reproducing kernel Hilbert space and its multiplication operatorsin Complex Analysis and Related Topics ed by E Ramirez de Arellano et al OperatorTheory Advances and Applications vol 114 (Birkhaumluser Basel 2000) pp 254ndash263

[575] FH Szafraniec Multipliers in the reproducing kernel Hilbert space subnormality andnoncommutative complex analysis in Reproducing Kernel Spaces and Applications edby D Alpay Operator Theory Advances and Applications vol 143 (Birkhaumluser Basel2003) pp 313ndash331

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[577] MC Teich BEA Saleh Squeezed states of light Quantum Opt 1 152ndash191 (1989)[578] R Terrier L Demanet IA Grenier J-P Antoine Wavelet analysis of EGRET data in

Proceedings of the 27th International Cosmic Ray Conference (ICRC 2001) (CopernicusGesellschaft DE 2001) pp 2923ndash2926

[579] T Thiemann Gauge field theory coherent states (GCS) 1 General properties Class QuantGrav 18 2025ndash2064 (2001)

[580] T Thiemann O Winkler Gauge field theory coherent states (GCS) 2 Peakednessproperties Class Quant Grav 18 2561ndash2636 (2001)

[581] T Thiemann O Winkler Gauge field theory coherent states (GCS) 3 Ehrenfest theoremsClass Quant Grav 18 4629ndash4682 (2001)

[582] T Thiemann O Winkler Gauge field theory coherent states (GCS) 4 Infinite tensorproduct and thermodynamical limit Class Quant Grav 18 4997ndash5054 (2001)

[583] K Thirulagasanthar ST Ali Regular subspaces of a quaternionic Hilbert space fromquaternionic Hermite polynomials and associated coherent states J Math Phys 54013506 (2013)

[584] K Thirulogasanthar G Honnouvo A Krzyzak Coherent states and Hermite polynomialson quaternionic Hilbert spaces J Phys A Math Theor 43 385205 (2010)

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group J Math Phys 32 1273ndash1279 (1991)[587] B Torreacutesani Time-frequency representation Wavelet packets and optimal decomposition

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341ndash346 (2005)[589] DA Trifonov Generalized intelligent states and squeezing J Math Phys 35 2297ndash2308

(1994)[590] AS Trushechkin IV Volovich Localization properties of squeezed quantum states in

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algorithms IEEE Trans Image Proc 11 363ndash372 (2002)[593] P Vandergheynst J-P Antoine E Van Vyve A Goldberg I Doghri Modelling and

simulation of an impact test using wavelets analytical and finite element models Int JSolids Struct 38 5481ndash5508 (2001)

[594] L Vanhamme RD Fierro S Van Huffel R de Beer Fast removal of residual water inproton spectra J Magn Reson 132 197ndash203 (1998)

[595] J Ville Theacuteorie et applications de la notion de signal analytique Cacircbles et Trans 2 61ndash74(1948)

[596] J Voisin On some unitary representations of the Galilei group I Irreducible representa-tions J Math Phys 6 1519ndash1529 (1965)

[597] A Vourdas Analytic representations in quantum mechanics J Phys A Math Gen 39R65ndashR141 (2006)

[598] DF Walls Squeezed states of light Nature 306 141ndash146 (1983)[599] YK Wang FT Hioe Phase transition in the Dicke maser model Phys Rev A 7 831ndash836

(1973)[600] PSP Wang J Yang A review of wavelet-based edge detection methods Int J Patt

Recogn Artif Intell 26 1255011 (2012)[601] I Weinreich A construction of C1-wavelets on the two-dimensional sphere Appl Comput

Harmon Anal 10 1ndash26 (2001)[602] H Weyl Quantenmechanik und Gruppentheorie Z Phys 46 1ndash46 (1927)

References 571

[603] Y Wiaux L Jacques P Vandergheynst Correspondence principle between spherical andEuclidean wavelets Astrophys J 632 15ndash28 (2005)

[604] Y Wiaux L Jacques P Vielva P Vandergheynst Fast directional correlation on the spherewith steerable filters Astrophys J 652 820ndash832 (2006)

[605] Y Wiaux JD McEwen P Vandergheynst O Blanc Exact reconstruction with directionalwavelets on the sphere Mon Not R Astron Soc 388 770ndash788 (2008)

[606] WM Wieland Complex Ashtekar variables and reality conditions for Holstrsquos action AnnHenri Poincareacute 13 425ndash448 (2012)

[607] EP Wigner On the quantum correction for thermodynamic equilibrium Phys Rev 40749ndash759 (1932)

[608] RM Willette RD Nowak Platelets A multiscale approach for recovering edges andsurfaces in photon-limited medical imaging IEEE Trans Med Imaging 22 332ndash350(2003)

[609] W Wisnoe P Gajan A Strzelecki C Lempereur J-M Matheacute The use of the two-dimensional wavelet transform in flow visualization processing in Progress in WaveletAnalysis and Applications (Proc Toulouse 1992) ed by Y Meyer S Roques (EdFrontiegraveres Gif-sur-Yvette 1993) pp 455ndash458

[610] K Woacutedkiewicz On the quantum mechanics of squeezed states J Modern Optics 34 941ndash948(1987)

[611] JA Yeazell M Mallalieu CR Stroud Jr Observation of the collapse and revival of aRydberg electronic wave packet Phys Rev Lett 64 2007ndash2010 (1990)

[612] JA Yeazell CR Stroud Jr Observation of fractional revivals in the evolution of aRydberg atomic wave packet Phys Rev A 43 5153ndash5156 (1991)

[613] HP Yuen Two-photon coherent states of the radiation field Phys Rev A 13 2226ndash2243(1976)

[614] J Zak Balian-Low theorem for Landau levels Phys Rev Lett 79 533ndash536 (1997)[615] J Zak Orthonormal sets of localized functions for a Landau level J Math Phys 39 4195ndash

4200 (1998) and references quoted there[616] AA Zakharova On the properties of generalized frames Math Notes 83 190ndash200 (2008)[617] W-M Zhang DH Feng R Gilmore Coherent states Theory and some applications Rev

Mod Phys 26 867ndash927 (1990)[618] I Zlatev W-M Zhang DH Feng Possibility that Schroumldingerrsquos conjecture for the

hydrogen atom coherent states is not attainable Phys Rev A 50 R1973ndashR1975 (1994)[619] WH Zurek Decoherence einselection and the quantum origins of the classical Rev Mod

Phys 75 715ndash775 (2003)[620] WH Zurek S Habib JP Paz Coherent states via decoherence Phys Rev Lett 70 1187ndash

1190 (1993)[621] K Zyczkowski Squeezed states in a quantum chaotic system J Phys A Math Theor 22

L1147ndashL1151 (1989)

Index

Symbolsν-selection 119

Aaction of semigroup on a lattice 395algorithm

best basis 384fast wavelet 385 439matching pursuit 498 521pyramidal 382 393

angular selectivity 427 443Apollonius 477applications of CS

in atomic physics 175 243in nuclear physics 178

applications of CWTin 1-D 368in 2-D 429

applications of DWTin 1-D 385in 2-D 436

area preserving projections 483

Bbundle

(co)tangent 251normal 251parallel 268

Ccanonical commutation relations (CCR) 16coboundaries 403cochains 402cocycle 63 69 72 260 393 403cocycle equation 398 404

coherent states (CS) 124action-angle 157 325atomic 243Barut-Girardello 3

of SU(11) 299canonical 2 15 19 169classical theory 174covariant 166 180deformed 146for infinite square well and Poumlschl-Teller

potentials 158for semidirect products 260Gazeau-Klauder 151generalized 11Gilmore-Perelomov 10 168

of SU(11) 81 296 297HilbertClowast-modules 164holomorphic 140nonholomorphic 151nonlinear 146of affine Galilei group 505of affine Poincareacute group 509of affine Weyl-Heisenberg group GaWH

497of compact semisimple Lie groups 174of Euclidean group E(n) 266of Galilei group G (11) 290of isochronous Galilei group 237of non-semisimple Lie groups 179of noncompact semisimple Lie groups 177of Poincareacute group Puarr

+(11) 283massless case 288

of Poincareacute group Puarr+(13) 279

of Schroumldinger group 508quasi-coherent states 186quaternionic 164


573

574 Index

coherent states (CS) (cont)spin or SU(2) 175square integrable covariant 166 180 264vector (VCS) 73 108 112 170weighted 184 523

of affine Weyl-Heisenberg group GaWH497


cohomology group 393 403coboundaries 403cochains 402cocycle 403

continuous WTin n-D 414in 1-D 353

applications 368continuous wavelet packets 385discretization 365 404 407localization properties 363

in 2-D 414applications 429as a symmetry scanner 432continuous wavelet packets 439interpretation 426representations 426resolving power 427 443

on conic sections 477on manifolds 510on surfaces of revolution 482on the sphere S

n 479on the sphere S

2 458Euclidean limit 462

on the torus T2 481contourlet transform 450coorbit theory 455curvelet transform

continuous 447discrete 449

Ddecomposition

Cartan 76 96Gauss 97 459Iwasawa 97 459 479

dictionary 455 498dilation

natural 396pseudodilation

associated 398on Zp 392principal 397

stereographic 458

discrete WTin 1-D 379

applications 385generalizations 384

in 2-D 434applications 436

on the sphere S2 471

Duflo-Moore operator 215 219 222 224 226239 286

dyadic lattice 381 519

Eevaluation map 25 121 125

FFibonacci numbers 388filters 382

compatible 399on Zp 393

pseudo-QMF 387QMF 382

Fourier transform 351 412relativistic 223

fractals 364frame 40

affine Weyl-Heisenberg CS 497discrete 54 365

for affine Poincareacute group 521for affine Weyl-Heisenberg group 521for Poincareacute group Puarr

+(11) 527

for Poincareacute group Puarr+(13) 534

for semidirect products 524Gabor or canonical CS 516wavelet 519

discretization 515 519finite 334for semidirect product 269fusion 57Galilei CS 291Littlewood-Paley 442Poincareacute CS 279tight 43 356

frame operator 40free orbit 217

GGabor analysis 5Gabor transform 349gaborettes 349gaussons 17 246

Index 575

golden mean τ 387 432τ-Haar basis 388τ-integers 388

group (abstract)direct product 98extension 99hypergroup 423locally compact abelian (LCA) 86

lattice in 88sampling in 89

semidirect product 98 217unimodular 62

group (explicit)GL(nR) 217SL(2R) SOo(12) SU(11) 3affine 12 351affine Galilei 504affine Poincareacute = SIM(n1) 509affine Poincareacute = SIM(11) 222affine Weyl-Heisenberg GaWH 495Anti-de Sitter SOo(12) 292Bessel-Kingman hypergroup 423 437connected affine or ax+b 12 67 209 355discrete Weyl-Heisenberg GN

dWH 518Euclidean E(2) E(n) 266extended Heisenberg 503Gut (upper-triangular matrices) 63Galilei 231 291Galilei-Schroumldinger 506isochronous Galilei 233metaplectic Mp(2nR) 246Poincareacute Puarr

+(11) 282

Poincareacute Puarr+(13) 271

Schroumldinger 503shearlet groups 450 454 503similitude group SIM(n) 225 412similitude group SIM(2) 221Stockwell 503symplectic Sp(2nR) 246Weyl-Heisenberg GWH 21 22 246 511

HHankel transform 437Hilbert space

direct integral of 116measurable field of 115 121reproducing kernel 10reproducing kernel mdash 180 206 227 230reproducing kernel mdash 23 108 115 117

121 126 130rigged mdash 183rigged mdash 48

holomorphic map 129hypergroup 423

Iintermittency measure 365

LLie algebra 91

contraction 101 293root 91weight 92

Lie group 93(co)adjoint action 94 251 253

of Sp(2nR) 248coadjoint orbit 95 252 297

of SIM(n) 415contraction 102

SOo(31) to SIM(2) 462SU(11) to Puarr

+(11) 294exponential map 94

lifting scheme 384localization 358 363localization operators 25

Mmanifold

Kaumlhler 34symplectic 34 251

measure(quasi-)invariant 62 78 180

on cotangent bundle 256Borel 38Haar 204positive operator-valued (POV) 25 39

commutative 40examples of 41Naımark extension theorem 42

projection-valued (PV) 40scale-angle 432

minimal uncertainty states 16model

Hepp-Lieb 175nuclear collective 178

modular function 62molecule

curvelet 456parabolic 456shearlet 456

moment problem 143motion analysis 499

576 Index

multiresolution analysis 380 393 395 400484

Haar 402on the sphere S

2 471spline 402

NNMR spectroscopy 370

Oobservables 307orthogonality relations 212 219 228 238

285 286overcomplete set 24

Pphase space 25 273 282 284 289ndash291 297

362polynomials

Hermite 149Pollaczek 149

POV function 108 122 126POV measure (POVM) 39 320pseudodilations 392

Qquantization 35 306 518

bounded motions 342coherent state (CS) 309covariant integral 314

Weyl-Heisenberg 316 323frame 333integral 313motion on the circle 339quantizable distributions 328quantizable functions 325

Rreconstruction

formula 208 215 356 415operator 356 360 361

representationdiscrete series 204

of SU(11) 76Fock-Bargmann 28induced 70 227 230 260 264

of SU(11) 78of semidirect products 259

regular 83 206 207

square integrable 204 206 219 260 352413 451

square integrable mod (H) 167square integrable mod (Hσ) 167 180

227 264 269 290 460reproducing kernel 10 80 124 125 180 206

227 230 356 415holomorphic 138square integrable 134

resolution of the identity 3 20 81 204 206227 230 241 264 356 415

resolution operator 40 180for Poincareacute Puarr

+(13) CS 275ridgelet transform 445ridges in WT 367

Ssampling 391 407 536

in LCA group 89scaling function 380 405Schroumldinger 1 506section 4 63 166 180

affine 274affine admissible 267Galilean 274 280 285 290Lorentz 280 285principal 256 280quasi-section 186 289symmetric 281 285

semi-frame 46 183continuous 183discrete 54fusion 60lower 46 49 462upper 46 49

shearlet transformcontinuous 452 454discrete 453

Short-Time Fourier Transform 349skeleton of WT 367space

coset or homogeneous 4coset or homogeneous mdash 166 180coset or homogeneous mdash 22 62Fock-Bargmann 28 296Hardy 355Krein 287

square integrability 9squeezed states 17 246subband coding scheme 383 400subspace

V -admissible 229cyclic 171

Index 577

symbols 6system of covariance 72system of imprimitivity 72

Ttempered distributions 357theorem

Balian-Low mdash 517Mackey imprimitivity mdash 72Naımark extension mdash 42Pontrjagin duality mdash 88Schur lemmas 84

time-frequency representation 348transform

Berezin 324contourlet 450curvelet 447Gabor 349ridgelet 445shearlet 452wavelet 349wedgelet 455Zak 518

Uuncertainty relations 16 423 516uniform grids on surfaces of revolution 486

Vvector

α-admissible 227admissible 204 352 413 451admissible mod (Hσ) 167 291 460

Wwavefront set 452wavelet bases

biorthogonal 384orthonormal 381

wavelet packets 384continuous 439

wavelet transform (WT) 349n-D continuous (CWT) 4141-D continuous (CWT) 353

1-D discrete (DWT) 3792-D continuous (CWT) 4232-D discrete (DWT) 434integer 384local 489of distributions 361of Schwartz functions 360on Zp 391 392on a graph 493

wavelet(s) 5 211 352τ-wavelets 387n-D Mexican hat 416n-D Morlet 4171-D Mexican hat Marr 3531-D Morlet 3542-D Cauchy 4193-D Cauchy 420on Zp 390

pseudodilations 392on LCA group 394 406

cohomological interpretation 402compatible filters 395 400

algebraic 387Cauchy 418Cauchy-Paul 354 419 425conical 418difference 417 462directional 416 440kinematical 499local 488metabolite-based 355 374minimal uncertainty 425multiselective 440on a graph 493on the sphere S

2 458on the sphere S

n 479on the torus T2 481steerable 439von Mises 440

wedgelet transform 455Wigner function 322Wigner-Ville transform 349Windowed Fourier or Gabor transform 349

ZZak transform 518

References

A Books and Theses

B Articles

Index

542 References

[Ber99] JC van den Berg (ed) Wavelets in Physics (Cambridge University Press Cambridge1999)

[Ber98] G Bernuau Proprieacuteteacutes spectrales et geacuteomeacutetriques des quasicristaux Ondelettesadapteacutees aux quasicristaux Thegravese de Doctorat CEREMADE Universiteacute Paris IXDauphine France 1998

[Bie81] L Biedenharn JD Louck The Racah-Wigner Algebra in Quantum Theory Ency-clopaedia of Mathematics vol 9 (Addison-Wesley Reading MA 1981)

[Bis10] S Biskri Deacutetection et analyse des boucles magneacutetiques solaires par traitementdrsquoimages Thegravese de Doctorat UST Houari Boumediegravene Alger 2010

[Bog05] I Bogdanova Wavelets on non-Euclidean manifolds PhD thesis EPFL 2005[Bog74] J Bognar Indefinite Inner Product Spaces (Springer Berlin 1974)[Bor72] A Borel Repreacutesentations des groupes localement compacts Lecture Notes in

Mathematics vol 276 (Springer Berlin 1972)[Bou93] K Bouyoucef Sur des aspects multireacutesolution en reconstruction drsquoimages Applica-

tion au Teacutelescope Spatial de Hubble Thegravese de Doctorat Univ P Sabatier Toulouse1993

[Bou97] A Bouzouina Comportement semi-classique de symplectomorphismes du tore quan-tifieacutes Thegravese de Doctorat Univ Paris-Dauphine 1997

[Bus91] P Busch PJ Lahti P Mittelstaedt The Quantum Theory of Measurement (SpringerBerlin and Heidelberg 1991)

[Can98] EJ Candegraves Ridgelets Theory and applications PhD thesis Department of Statis-tics Stanford University 1998

[Chr03] O Christensen An Introduction to Frames and Riesz Bases (Birkhaumluser BaselBoston Berlin 2003)

[Chu92] CK Chui An Introduction to Wavelets (Academic San Diego 1992)[Coh77] C Cohen-Tannoudji B Diu F Laloeuml Meacutecanique Quantique Tome I (Hermann

Paris 1977)[Com90] J-M Combes A Grossmann P Tchamitchian (eds) Wavelets Time-Frequency

Methods and Phase Space (Proc Marseille 1987) 2nd edn (Springer Berlin 1990)[Com12] M Combescure D Robert Shape Analysis and Classification Theory and Practice

(Springer Dordrecht Heidelberg 2012)[Cos01] LF Costa RM Cesar Jr Coherent States and Applications in Mathematical Physics

(CRC Press Boca Raton FL 2001)[Dau92] I Daubechies Ten Lectures on Wavelets (SIAM Philadelphia 1992)[Dav90] EB Davies Heat Kernels and Spectral Theory (Cambridge University Press Cam-

bridge 1990)[DeV88] R De Valois K De Valois Spatial Vision (Oxford University Press New York 1988)

[Dir01] PAM Dirac Lectures on Quantum Mechanics (Dover New York 2001)[Dix64] J Dixmier Les C-algegravebres et leurs repreacutesentations (Gauthier-Villars Paris 1964)[Dod03] VV Dodonov VI Manrsquoko (eds) Theory of Nonclassical States of Light (Taylor and

Francis London New York 2003)[Duv91] M Duval-Destin Analyse spatiale et spatio-temporelle de la stimulation visuelle agrave

lrsquoaide de la transformeacutee en ondelettes Thegravese de Doctorat Universiteacute drsquoAix-MarseilleII 1991

[Fea90] J-C Feauveau Analyse multireacutesolution par ondelettes non orthogonales et bancs defiltres numeacuteriques Thegravese de Doctorat Universiteacute Paris-Sud 1990

[Fei98] HG Feichtinger T Strohmer (eds) Gabor Analysis and Algorithms ndash Theory andApplications (Birkhaumluser Boston-Basel-Berlin 1998)

[Fei01] HG Feichtinger T Strohmer (eds) Advances in Gabor Analysis (BirkhaumluserBoston 2001)

[Fen94] DH Feng JR Klauder M Strayer (eds) Coherent States Past Present and Future(Proc Oak Ridge 1993) (World Scientific Singapore 1994)

[Fla98] P Flandrin Temps-Freacutequence (Hermegraves Paris 1993) Engliah translation Time-FrequencyTime-Scale Analysis (Academic New York 1998)

References 543
























544 References


























References 545

























Wellesley MA 1994)

546 References





B Articles

















References 547


























548 References

























References 549
























550 References

























References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























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L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 543
























544 References


























References 545

























Wellesley MA 1994)

546 References





B Articles

















References 547


























548 References

























References 549
























550 References

























References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

544 References


























References 545

























Wellesley MA 1994)

546 References





B Articles

















References 547


























548 References

























References 549
























550 References

























References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 545

























Wellesley MA 1994)

546 References





B Articles

















References 547


























548 References

























References 549
























550 References

























References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

546 References





B Articles

















References 547


























548 References

























References 549
























550 References

























References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 547


























548 References

























References 549
























550 References

























References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

548 References

























References 549
























550 References

























References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 549
























550 References

























References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

550 References

























References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 551

























552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

552 References



























References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 553

























554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

554 References


























References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 555



























556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

556 References























References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 557

























558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

558 References


























References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 559

























560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

560 References























References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 561

























Appl 13 405ndash419 (2007)

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

562 References
























References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 563

























564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

564 References

























References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 565
























566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

566 References
























References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 567


























568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

568 References

























References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 569

























570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

570 References



























References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

References 571


















L1147ndashL1151 (1989)

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

Index









Bbundle












573

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

574 Index













Ddecomposition





stereographic 458















+(11) 527






Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

Index 575







+(11) 282








LLie algebra 91








Mmanifold











576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

576 Index



2 471spline 402





362polynomials






Rreconstruction





regular 83 206 207

















Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

Index 577







Vvector














ZZak transform 518

References

A Books and Theses

B Articles

Index

a. books and theses€¦ · references a. books and theses [abr97] p. abry, ondelettes et...

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