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

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

2005-06-17

arxiv.org/abs/math/0506345v1

Int. Math. Res. Not. 2005, 1817--1831.

Mathematics

Classical Analysis and ODEs

9 pp., LaTeX, no figures; final version, to appear in Int. Math. Res. Not

Scientific paper

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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