viorel catana university politehnica of bucharest department of mathematics i

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Weyl transforms and the generalized Hermite operator.The abstract Cauchy problem (ACP) for the abstract Hermite operator. Viorel Catana University Politehnica of Bucharest Department of Mathematics I catana_viorel@yahoo.co.uk. The 10th French-Romanian Conference on Applied Mathematics - PowerPoint PPT Presentation

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  • Weyl transforms and the generalized Hermite operator.The abstract Cauchy problem (ACP) for the abstract Hermite operator.Viorel Catana University Politehnica of Bucharest Department of Mathematics Icatana_viorel@yahoo.co.ukThe 10th French-Romanian Conference on Applied Mathematics

    Poitiers (Futuroscope ) ,France , August 26-31 , 2010

  • TopicsIntroductionBasic definitions and notationsPreliminary results The generalized Hermite semigroupThe inverse of the generalized Hermite operatorThe heat kernel of the generalized Hermite operatorThe Green function of the generalized Hermite operator Global hypoellipticityUltracontractivity and HypercontractivityThe abstract Hermite semigroupThe abstract Cauchy problem (ACP) for the abstract Hermite operator

  • Introduction

  • References

  • The twisted Laplacian

  • Wongs research about twisted Laplacian

  • Basic definitions & notations

  • The generalized Hermite operator

  • Basic transformations

  • The generalized Hermite functions

  • Preliminary results

  • Main results concerning the Hermite semigroup

  • For the proof of Theorem 6 we need the following two results (see Chapter 17 of the book [17] and Theorem 15.4 and Theorem 17.1 in the book [16] by Wong).

  • The inverse of the generalized Hermite operator

  • The heat kernel

  • Preliminary result

  • The Green function of the generalized Hermite operator

  • Global hypoellipticity

  • Ultracontractivity and Hypercontractivity

  • The abstract Cauchy problem (ACP) for the abstract Hermite operator

  • The abstract Hermite operator

  • The semigroup of the abstract Hermite operator

  • An estimate of the abstract Hermite semigroup

  • The (ACP) for the abstract Hermite operator

  • Merci pour votre aimable attention!

    Thank you for your kind attention!