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An elementary proof of the positivity of the intertwining operator in one-dimensional trigonometric Dunkl theory


Author: Jean-Philippe Anker
Journal: Proc. Amer. Math. Soc. 146 (2018), 189-193
MSC (2010): Primary 33C67
DOI: https://doi.org/10.1090/proc/13679
Published electronically: August 1, 2017
MathSciNet review: 3723132
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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
Email: anker@univ-orleans.fr

DOI: https://doi.org/10.1090/proc/13679
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
Article copyright: © Copyright 2017 American Mathematical Society