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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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An elementary proof of the positivity of the intertwining operator in one-dimensional trigonometric Dunkl theory
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by Jean-Philippe Anker PDF
Proc. Amer. Math. Soc. 146 (2018), 189-193 Request permission

Abstract:

This note is devoted to the intertwining operator in the one-dimensional trigonometric Dunkl setting. We obtain a simple integral expression of this operator and deduce its positivity.
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Additional Information
  • Jean-Philippe Anker
  • Affiliation: Université Orléans & CNRS, Fédération Denis Poisson (FR 2964), Laboratoire MAPMO (UMR 7349), Bâtiment de Mathématiques, B.P. 6759, 45067 Orléans cedex 2, France
  • MR Author ID: 198768
  • Email: anker@univ-orleans.fr
  • Received by editor(s): November 20, 2016
  • Received by editor(s) in revised form: January 18, 2017, and January 29, 2017
  • Published electronically: August 1, 2017
  • Additional Notes: This work was partially supported by the regional project MADACA (Marches Aléatoires et processus de Dunkl–Approches Combinatoires et Algébriques, www.fdpoisson.fr/madaca).
  • Communicated by: Mourad E. H. Ismail
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 189-193
  • MSC (2010): Primary 33C67
  • DOI: https://doi.org/10.1090/proc/13679
  • MathSciNet review: 3723132