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Relating transplantation and multipliers for Dunkl and Hankel transforms

✍ Scribed by Adam Nowak; Krzysztof Stempak

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 125 KB
Volume: 281
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200510700

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✦ Synopsis

Abstract

By expressing the Dunkl transform of order α of a function f in terms of the Hankel transforms of orders α and α + 1 of even and odd parts of f, respectively, we show that a considerable part of harmonic analysis of the Dunkl transform on the real line may be reduced to known results for the Hankel transform. In particular, defining the modified Dunkl transform and then considering the Dunkl transplantation operator we transfer known multiplier results for the Hankel transform to the Dunkl transform setting. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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