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.
Domaines
Analyse fonctionnelle [math.FA]
Origine : Fichiers produits par l'(les) auteur(s)
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