viorel catana university politehnica of bucharest department of mathematics i

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!