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Licensed Unlicensed Requires Authentication Published by De Gruyter January 19, 2012

Opdam's hypergeometric functions: product formula and convolution structure in dimension 1

  • Jean-Philippe Anker EMAIL logo , Fatma Ayadi and Mohamed Sifi

Abstract.

Let G(,) be the eigenfunctions of the Dunkl–Cherednik operator T(,) on . In this paper we express the product G(,)(x)G(,)(y) as an integral in terms of G(,)(z) with an explicit kernel. In general this kernel is not positive. Furthermore, by taking the so-called rational limit, we recover the product formula of M. Rösler for the Dunkl kernel. We then define and study a convolution structure associated to G(,).

Received: 2010-04-30
Revised: 2011-04-12
Published Online: 2012-01-19
Published in Print: 2012-January

© 2012 by Walter de Gruyter Berlin Boston

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