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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Editorial Board: 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

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1869-6090
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Dunkl kernel and Dunkl translation for a positive subsystem of orthogonal roots

Luc Deleaval
Published Online: 2013-06-05 | DOI: https://doi.org/10.1515/apam-2012-0013

Abstract.

In this article, we give an explicit formula for the Dunkl kernel associated with a positive subsystem of orthogonal roots. We then prove a product formula for this kernel which allows us to show that the Dunkl translation is a bounded operator in this setting. We finally study the Dunkl maximal operator for such subsystems.

Keywords: Dunkl operators; Dunkl kernel; special function; maximal operator

About the article

Received: 2012-06-11

Accepted: 2013-02-09

Published Online: 2013-06-05

Published in Print: 2013-06-01


Citation Information: Advances in Pure and Applied Mathematics, Volume 4, Issue 2, Pages 107–137, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2012-0013.

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© 2013 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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[1]
L. Deleaval, N. Demni, and H. Youssfi
Journal of Mathematical Analysis and Applications, 2015, Volume 432, Number 2, Page 928

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