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Elementary proofs of Paley-Wiener theorems for the Dunkl transform on the real line

Nils Byrial Andersen·Marcel de Jeu
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Abstract

We give an elementary proof of the Paley-Wiener theorem for smooth functions for the Dunkl transforms on the real line, establish a similar theorem for L^2-functions and prove identities in the spirit of Bang for L^p-functions. The proofs seem to be new also in the special case of the Fourier transform.

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BibTeXRIS

Nils Byrial Andersen, Marcel de Jeu. 2005-06-17. Elementary proofs of Paley-Wiener theorems for the Dunkl transform on the real line. https://doi.org/10.1155/imrn.2005.1817

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