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Keywords:
Dunkl-Hermite functions; Dunkl-Hermite semigroup; Dunkl-Hermite-Sobolev space
Dunkl-Hermite functions; Dunkl-Hermite semigroup; Dunkl-Hermite-Sobolev space
Summary:
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 $L^p_\alpha(\mathbb{R})$, $1<p<\infty$, 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.
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