Korean J. Math. Vol. 24 No. 4 (2016) pp.693-722
DOI: https://doi.org/10.11568/kjm.2016.24.4.693

Spectral theorems associated to the Dunkl operators

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Published: Dec 30, 2016
Keywords:
Dunkl transform, Dunkl resolvent function, real Paley-Wiener theorem, Roe's theorem.
Mathematics Subject Classification:
44A05, 42B10.

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Hatem Mejjaoli
Department of Mathematics Taibah University Al Madinah AL Munawarah 30002, Saudi Arabia.

Abstract

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.


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References

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