Images of some functions and functional spaces under the Dunkl-Hermite semigroup

Néjib Ben Salem; Walid Nefzi

Displaying similar documents to “Images of some functions and functional spaces under the Dunkl-Hermite semigroup”

A note on locally inverse semigroup algebras.

Guo, Xiaojiang (2008)

International Journal of Mathematics and Mathematical Sciences

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An analogue of Gutzmer's formula for Hermite expansions

S. Thangavelu (2008)

Studia Mathematica

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We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of L²(ℝⁿ) under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.

On analyticity of Ornstein-Uhlenbeck semigroups

Beniamin Goldys (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $(R_{t}$ be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let $μ$ denote its Gaussian invariant measure. We show that the semigroup $(R_{t}$ is analytic in $L^{2} (μ)$ if and only if its generator is variational. In particular, we show that the transition semigroup of a finite dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.