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Spectral theorems associated to the Dunkl operators

Hatem Mejjaoli
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2016.12|한국수학논문집 (Korean Journal of Mathematics)|제24권 제4호|pp. 693-722|DOI https://doi.org/10.11568/kjm.2016.24.4.693

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키워드

Dunkl transformDunkl resolvent functionreal Paley-Wiener theoremRoe's theorem.
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초록

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.

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.

참고문헌 (24)

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