Geodesic
Images of some functions and functional spaces under the Dunkl-Hermite semigroup
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 345-365

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We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, $\mathcal{S}(\mathbb{R})$ and $L^p_\alpha(\mathbb{R})$, $1$, under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.
Classification : 42B25, 46E35, 47B38, 47D03
Keywords: Dunkl-Hermite functions; Dunkl-Hermite semigroup; Dunkl-Hermite-Sobolev space 
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Ben Salem, Néjib; Nefzi, Walid. Images of some functions and functional spaces under the Dunkl-Hermite semigroup. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 345-365. http://geodesic.mathdoc.fr/item/CMUC_2013__54_3_a3/