Fourier Analysis: An Introduction, 2011, 320 pages, Elias M. Stein, Rami Shakarchi,1400831237, 9781400831234, Princeton University Press, 2011

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This first volume, a three-part introduction to the subject, is intended for students with a beginningknowledge of mathematical analysis who are motivated to discover the ideas that shape Fourieranalysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth centurywhen studying problems in the physical sciences--that an arbitrary function can be written as aninfinite sum of the most basic trigonometric functions. The first part implements this idea in termsof notions of convergence and summability of Fourier series, while highlighting applications such asthe isoperimetric inequality and equidistribution. The second part deals with the Fourier transformand its applications to classical partial differential equations and the Radon transform; a clearintroduction to the subject serves to avoid technical difficulties. The book closes with Fouriertheory for finite abelian groups, which is applied to prime numbers in arithmetic progression. Inorganizing their exposition, the authors have carefully balanced an emphasis on key conceptualinsights against the need to provide the technical underpinnings of rigorous analysis. Students ofmathematics, physics, engineering and other sciences will find the theory and applications coveredin this volume to be of real interest. The Princeton Lectures in Analysis represents a sustainedeffort to introduce the core areas of mathematical analysis while also illustrating the organic unitybetween them. Numerous examples and applications throughout its four planned volumes, ofwhich Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas inanalysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move froman introduction addressing Fourier series and integrals to in-depth considerations of complexanalysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such asfunctional analysis, distributions and elements of probability theory.

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Intermediate Mathematical Analysis , Anthony E. Labarre, 2008, Mathematics, 253 pages. Focusingon concepts rather than techniques, this text deals primarily with real-valued functions of a realvariable. Complex numbers appear only in supplements and the last.

Fourier Analysis , T. W. Körner, Jan 28, 1988, Mathematics, 608 pages. Fourier analysis is asubject that was born in physics but grew up in mathematics. Now it is part of the standardrepertoire for mathematicians, physicists and engineers. In.

Real Analysis Measure Theory, Integration, and Hilbert Spaces, Elias M. Stein, Rami Shakarchi, Nov28, 2009, Mathematics, 392 pages. Real Analysis is the third volume in the Princeton Lectures inAnalysis, a series of four textbooks that aim to present, in an integrated manner, the core areas ofanalysis.

Discrete Fourier Analysis , M. W. Wong, May 30, 2011, Abstract Harmonic Analysis, 185 pages.This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Writtenin a concise style, it is interlaced with remarks, discussions and.

Problems and Solutions for Undergraduate Analysis With 40 Illustrations, Rami Shakarchi, 1998,Mathematics, 368 pages. This volume contains all the exercises and their solutions for Lang'ssecond edition of UNDERGRADUATE ANALYSIS. The wide variety of exercises, which range fromcomputational to.

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Invitation to Classical Analysis , Peter L. Duren, 2012, Mathematics, 392 pages. This book gives arigorous treatment of selected topics in classical analysis, with many applications and examples.The exposition is at the undergraduate level, building on.

An Introduction to Complex Analysis and Geometry , John P. D'Angelo, 2010, Mathematics, 163pages. .

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Harmonic Analysis From Fourier to Wavelets, MarГa Cristina Pereyra, Lesley A. Ward, Jan 1,2012, Mathematics, 410 pages. "In the last 200 years, harmonic analysis has been one of themost influential bodies of mathematical ideas, having been exceptionally significant both in itstheoretical.

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Introduction to Applied Mathematics , Lawrence Sirovich, Nov 9, 1988, Computers, 388 pages.From the Preface: "The material in this book is based on notes for a course which I gave severaltimes at Brown University. The target of the course was juniors and seniors.

Fourier analysis , Hwei Piao Hsu, 1970, Mathematics, 274 pages. .

Exercises in Fourier Analysis , T. W. Körner, Aug 19, 1993, Mathematics, 385 pages. Fourieranalysis is an indispensable tool for physicists, engineers and mathematicians. A wide variety ofthe techniques and applications of fourier analysis are discussed in.

Harmonic Analysis Real-variable Methods, Orthogonality, and Oscillatory Integrals, Elias M. Stein,Timothy S. Murphy, 1993, Mathematics, 695 pages. This book contains an exposition of some ofthe main developments of the last twenty years in the following areas of harmonic analysis:singular integral and pseudo.

Fourier analysis , Larry Baggett, Watson Fulks, 1979, Fourier analysis, 183 pages. .

Fourier Analysis , Javier Duoandikoetxea Zuazo, Jan 1, 2001, Mathematics, 222 pages. .

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