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

  • Jean-Philippe Anker EMAIL logo , Fatma Ayadi und Mohamed Sifi
Veröffentlicht/Copyright: 19. Januar 2012
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Advances in Pure and Applied Mathematics
Aus der Zeitschrift Band 3 Heft 1

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(,).

Keywords.: Dunkl–Cherednik operator; Opdam–Cherednik transform; product formula; convolution product; Kunze–Stein phenomenon
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

Artikel in diesem Heft

  1. Prelims
  2. Warfield invariants of normed unit groups in abelian group rings
  3. Opdam's hypergeometric functions: product formula and convolution structure in dimension 1
  4. On generalized Laplace equation and nonlinear operators
  5. Steady state solutions to the conserved Kuramoto–Sivashinsky equation
  6. Variational analysis for an indefinite quasilinear problem with variable exponent
  7. A probabilistic counterpart of the Askey scheme for continuous polynomials
  8. A characterisation of the Weyl transform
https://doi.org/10.1515/apam.2011.008
Schlagwörter für diesen Artikel
Dunkl–Cherednik operator; Opdam–Cherednik transform; product formula; convolution product; Kunze–Stein phenomenon

Artikel in diesem Heft

  1. Prelims
  2. Warfield invariants of normed unit groups in abelian group rings
  3. Opdam's hypergeometric functions: product formula and convolution structure in dimension 1
  4. On generalized Laplace equation and nonlinear operators
  5. Steady state solutions to the conserved Kuramoto–Sivashinsky equation
  6. Variational analysis for an indefinite quasilinear problem with variable exponent
  7. A probabilistic counterpart of the Askey scheme for continuous polynomials
  8. A characterisation of the Weyl transform
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