Viorel Catana University Politehnica of Bucharest Department of Mathematics I
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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
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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
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IntroductionIntroduction
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ReferencesReferences
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The twisted LaplacianThe twisted Laplacian
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Wong’s research about Wong’s research about twisted Laplaciantwisted Laplacian
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Basic definitions & notationsBasic definitions & notations
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The generalized Hermite The generalized Hermite operatoroperator
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Basic transformationsBasic transformations
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The generalized Hermite The generalized Hermite functionsfunctions
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Preliminary resultsPreliminary results
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Main results concerning the Main results concerning the Hermite semigroupHermite semigroup
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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).
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The inverse of the generalized The inverse of the generalized Hermite operatorHermite operator
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The heat kernelThe heat kernel
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Preliminary resultPreliminary result
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The Green function of the The Green function of the generalized Hermite generalized Hermite
operatoroperator
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Global hypoellipticityGlobal hypoellipticity
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Ultracontractivity and Ultracontractivity and HypercontractivityHypercontractivity
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The abstract Cauchy problem The abstract Cauchy problem (ACP) for the abstract Hermite (ACP) for the abstract Hermite
operatoroperator
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The abstract Hermite operatorThe abstract Hermite operator
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The semigroup of the abstract The semigroup of the abstract Hermite operatorHermite operator
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An estimate of the abstract An estimate of the abstract Hermite semigroupHermite semigroup
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The (ACP) for the abstract The (ACP) for the abstract Hermite operatorHermite operator
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Merci pour votre aimable Merci pour votre aimable attention!attention!
Thank you for your kind Thank you for your kind attention!attention!