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




A Paley-Wiener theorem about the spectral parameter, and a support theorem for general types of Dunkl spherical means - Download this document for free, or read online. Document in PDF available to download.

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Abstract : 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 $\overline{BO,R}.$ 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.





Author: Salem Ben Saïd -

Source: https://hal.archives-ouvertes.fr/



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