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Pré-Publication, Document De Travail Année : 2016

A Paley-Wiener theorem about the spectral parameter, and a support theorem for general types of Dunkl spherical means

Résumé

For $s\in \mathbb R,$ denote by $\cal P_k^s$ the ``projections" of a function $f$ in $\mathcal D(\mathbb R^d)$ into the eigenspaces of the Dunkl Laplacian $\Delta_k$ corresponding to the eigenvalue $-s^2.$ The parameter $k$ comes from Dunkl's theory of differential-difference operators. Wa shall characterize the range of $\cal P_k^s$ on the space of functions $f\in \mathcal D(\mathbb R^d)$ supported inside the closed ball $\overline{B(O,R)}.$ As a first application of this Paley-Wiener type theorem, we provide a spectral version of de Jeu's Paley-Wiener theorem for the Dunkl transform. The second application concerns a support theorem for general types of Dunkl spherical means.
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Dates et versions

hal-01282505 , version 1 (03-03-2016)

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  • HAL Id : hal-01282505 , version 1

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Salem Ben Saïd. A Paley-Wiener theorem about the spectral parameter, and a support theorem for general types of Dunkl spherical means. 2016. ⟨hal-01282505⟩
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