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

DOI10.1090/PROC/13679zbMath1384.33030arXiv1611.06872OpenAlexW2556889122MaRDI QIDQ4590976

Jean-Philippe Anker

Publication date: 21 November 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.06872

zbMATH Keywords

integral representationpositivitytrigonometric Dunkl theory

Mathematics Subject Classification ID

Hypergeometric functions associated with root systems (33C67)

Related Items (1)

An Introduction to Dunkl Theory and Its Analytic Aspects

Cites Work

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• Singularities and analytic continuation of the Dunkl and the Jacobi-Cherednik intertwining operators and their duals
• Lecture notes on Dunkl operators for real and complex reflection groups
• The positivity of the transmutation operators associated with the Cherednik operators attached to the root system of type \(A_{2}\)
• TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A CHEREDNIK TYPE OPERATOR ON THE REAL LINE
• POSITIVITY OF THE TRANSMUTATION OPERATORS AND ABSOLUTE CONTINUITY OF THEIR REPRESENTING MEASURES FOR A ROOT SYSTEM ON $\mathbb{R}^d$
• Positivity of the Jacobi–Cherednik intertwining operator and its dual
• Positivity of the transmutation operators associated with a Cherednik type operator on the real line
• The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory

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