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Mean-periodic functions associated with the Dunkl operators

Author： Salem N.B. Kallel S.

Publisher： Taylor & Francis Ltd

ISSN： 1065-2469

Source： Integral Transforms and Special Functions, Vol.15, Iss.2, 2004-04, pp. : 155-179

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

In this work, we consider the Dunkl operator on the real line , defined for by A C-function f on , is said to be mean-periodic function associated with the Dunkl operator D_k if there exists a nonzero distribution on with compact support such that where *_k denotes the convolution associated with the Dunkl operator D_k. We characterize the solutions of these equations and we study the expansion of a mean-periodic function in series with respect to appropriate exponential monomials. Finally, we give some applications.

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