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arXiv:math/0506345 [math.CA]AbstractReferencesReviewsResources

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

Nils Byrial Andersen, Marcel de Jeu

Published 2005-06-17Version 1

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.

Comments: 9 pp., LaTeX, no figures; final version, to appear in Int. Math. Res. Not
Journal: Int. Math. Res. Not. 2005, 1817--1831.
Categories: math.CA, math.RT
Subjects: 44A15, 42A38, 33C52
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