Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Editorial Board Member: Aldroubi, Akram / Anker, Jean-Philippe / Aouadi, Saloua / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Baraket, Sami / Ben Abdelghani, Leila / Begehr, Heinrich / Beznea, Lucian / Bezzarga, Mounir / Bonami, Aline / Demailly, Jean-Pierre / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jarboui, Noomen / Jouini, Elyes / Karoui, Abderrazek / Kamoun, Lotfi / Kobayashi, Toshiyuki / Maday, Yvon / Marzougui, Habib / Mili, Maher / Mustapha, Sami / Ovsienko, Valentin / Peigné, Marc / Pouzet, Maurice / Radulescu, Vicentiu / Schwartz, Lionel / Sifi, Mohamed / Zaag, Hatem / Zarati, Said

4 Issues per year


CiteScore 2016: 0.36

SCImago Journal Rank (SJR) 2016: 0.227
Source Normalized Impact per Paper (SNIP) 2016: 0.717

Mathematical Citation Quotient (MCQ) 2016: 0.28

Online
ISSN
1869-6090
See all formats and pricing
More options …

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

Jean-Philippe Anker
  • Université d'Orléans & CNRS, Fédération Denis Poisson (FR 2964), Laboratoire MAPMO (UMR 6628), B.P. 6759, 45067 Orléans cedex 2, France
  • Email:
/ Fatma Ayadi
  • Département de Mathématiques, Université de Tunis El Manar, 2092 Tunis El Manar, Tunisia; and Université d'Orléans & CNRS, Fédération Denis Poisson (FR 2964), Laboratoire MAPMO (UMR 6628), B.P. 6759, 45067 Orléans cedex 2, France
  • Email:
/ Mohamed Sifi
  • Département de Mathématiques, Université de Tunis El Manar, Faculté des Sciences de Tunis, 2092 Tunis El Manar, Tunisia
  • Email:
Published Online: 2012-01-19 | DOI: https://doi.org/10.1515/apam.2011.008

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

About the article

Received: 2010-04-30

Revised: 2011-04-12

Published Online: 2012-01-19

Published in Print: 2012-01-01


Citation Information: Advances in Pure and Applied Mathematics, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2011.008.

Export Citation

Comments (0)

Please log in or register to comment.
Log in