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TRIMÈCHE, Khalifa Department of Mathematics Faculty of Science of Tunis University Tunis El-Manar
We consider the transmutation operators Vk, tVk and V W k , tV W k associated respectively with the Cherednik operators and the Heckman-Opdam theory attached to the root system BC2, called also in [8, 9, 10] the trigonometric Dunkl intertwining operators, and their dual. In this paper we prove that the operators Vk, tVk and VWk , tVWk are positivity preserving and allows positive integral representations. In particular we deduce that the Opdam-Cherednik and the Heckman-Opdam kernels are positive definite.
Cherednik operators-Root system of type BC2
The trigonometric Dunkl intertwining operator and its dual
Mathematical Journal of Okayama University
Department of Mathematics, Faculty of Science, Okayama University
Copyright©2016 by the Editorial Board of Mathematical Journal of Okayama University