Spectral theorems associated to the Dunkl operators

Hatem Mejjaoli


In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The  behavior  of  the  sequence  of $L^{p}_{k}-$norms of  iterated   Dunkl potentials  is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on $\mathbb{R}^{d}$ for  distributions, in an elementary treatment based on the inversion theorem. Next, we  improve the Roe's theorem associated to the Dunkl operators.


Dunkl transform, Dunkl resolvent function, real Paley-Wiener theorem, Roe's theorem.

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DOI: http://dx.doi.org/10.11568/kjm.2016.24.4.693


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