The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman-Opdam theory on \(\mathbb{R}^d\)

DOI10.1515/apam-2016-0122zbMath1360.33017OpenAlexW2577773662MaRDI QIDQ520895

Khalifa Trimèche

Publication date: 6 April 2017

Published in: Advances in Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/apam-2016-0122

zbMATH Keywords

product formulasHeckman-Opdam hypergeometric functionhypergeometric translation operatorsOpdam-Cherednik kernel

Mathematics Subject Classification ID

Other functions coming from differential, difference and integral equations (33E30) Reflection groups, reflection geometries (51F15) Hypergeometric functions associated with root systems (33C67)

Related Items (1)

The hypergroup associated with the Cherednik operators and applications to the infinitely divisible probabilities and convolution semigroups

Cites Work

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• Harmonic analysis for certain representations of graded Hecke algebras
• A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras
• Contributions to the hypergeometric function theory of Heckman and Opdam: Sharp estimates, Schwartz space, heat kernel
• Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory
• POSITIVITY OF THE TRANSMUTATION OPERATORS AND ABSOLUTE CONTINUITY OF THEIR REPRESENTING MEASURES FOR A ROOT SYSTEM ON $\mathbb{R}^d$
• The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory

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