THE POSITIVITY OF THE HYPERGEOMETRIC
TRANSLATION OPERATORS ASSOCIATED TO
THE CHEREDNIK OPERATORS AND
THE HECKMAN-OPDAM THEORY ATTACHED
TO THE ROOT SYSTEM OF TYPE BC2
Khalifa Trimèche
Department of Mathematics
Faculty of Sciences of Tunis
University of Tunis El Manar
Campus, 2092 - Tunis, TUNISIA

Abstract

We consider the hypergeometric translation operator associated to the Cherednik operators and the Heckman-Opdam theory attached to the root system of type BC2. We prove in this paper that these operators are positivity preserving and allows positive integral representations. In particular we deduce that the product formulas of the Opdam-Cherednik kernel and the Heckman-Opdam hypergeometric function are positive integral transforms, and we obtain best estimates of these kernels.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 29
Issue: 6
Year: 2016

DOI: 10.12732/ijam.v29i6.4

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