Weyl transforms and the generalized Weyl transforms and the generalized Hermite operator.The abstract Hermite operator.The abstract Cauchy problem (ACP) for the Cauchy problem (ACP) for the
abstract Hermite operator.abstract Hermite operator.
Viorel Catana Viorel Catana University Politehnica of Bucharest University Politehnica of Bucharest
Department of Mathematics IDepartment of Mathematics [email protected][email protected]
The 10th French-Romanian Conference on Applied Mathematics
Poitiers (Futuroscope ) ,France , August 26-31 , 2010
TopicsTopics
IntroductionIntroduction Basic definitions and notationsBasic definitions and notations Preliminary results Preliminary results The generalized Hermite semigroupThe generalized Hermite semigroup The inverse of the generalized Hermite operatorThe inverse of the generalized Hermite operator The heat kernel of the generalized Hermite operatorThe heat kernel of the generalized Hermite operator The Green function of the generalized Hermite The Green function of the generalized Hermite
operator operator Global hypoellipticityGlobal hypoellipticity Ultracontractivity and HypercontractivityUltracontractivity and Hypercontractivity The abstract Hermite semigroupThe abstract Hermite semigroup The abstract Cauchy problem (ACP) for the abstract The abstract Cauchy problem (ACP) for the abstract
Hermite operatorHermite operator
IntroductionIntroduction
ReferencesReferences
The twisted LaplacianThe twisted Laplacian
Wong’s research about Wong’s research about twisted Laplaciantwisted Laplacian
Basic definitions & notationsBasic definitions & notations
The generalized Hermite The generalized Hermite operatoroperator
Basic transformationsBasic transformations
The generalized Hermite The generalized Hermite functionsfunctions
Preliminary resultsPreliminary results
Main results concerning the Main results concerning the Hermite semigroupHermite semigroup
For the proof of Theorem 6 we need the following two results (see 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 Chapter 17 of the book [17] and Theorem 15.4 and Theorem 17.1 in the
book [16] by Wong).book [16] by Wong).
The inverse of the generalized The inverse of the generalized Hermite operatorHermite operator
The heat kernelThe heat kernel
Preliminary resultPreliminary result
The Green function of the The Green function of the generalized Hermite generalized Hermite
operatoroperator
Global hypoellipticityGlobal hypoellipticity
Ultracontractivity and Ultracontractivity and HypercontractivityHypercontractivity
The abstract Cauchy problem The abstract Cauchy problem (ACP) for the abstract Hermite (ACP) for the abstract Hermite
operatoroperator
The abstract Hermite operatorThe abstract Hermite operator
The semigroup of the abstract The semigroup of the abstract Hermite operatorHermite operator
An estimate of the abstract An estimate of the abstract Hermite semigroupHermite semigroup
The (ACP) for the abstract The (ACP) for the abstract Hermite operatorHermite operator
Merci pour votre aimable Merci pour votre aimable attention!attention!
Thank you for your kind Thank you for your kind attention!attention!