Journal Article The positivity of the transmutation operators associated to the Cherednik operators for the root system $BC_2$

TRIMÈCHE, Khalifa

58 ( 1 )  , pp.183 - 198 , 2016-01 , Department of Mathematics, Faculty of Science, Okayama University
ISSN:0030-1566
NCID:AA00723502
Description
We consider the transmutation operators V<sub>k</sub>, <sup>t</sup>V<sub>k</sub> and V <sup>W</sup> <sub>k</sub> , <sup>t</sup>V <sup>W</sup> <sub>k</sub> 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 V<sub>k</sub>, <sup>t</sup>V<sub>k</sub> and V<sup>W</sup><sub>k</sub> , <sup>t</sup>V<sup>W</sup><sub>k</sub> are positivity preserving and allows positive integral representations. In particular we deduce that the Opdam-Cherednik and the Heckman-Opdam kernels are positive definite.
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http://ousar.lib.okayama-u.ac.jp/files/public/5/53925/20160528120812759385/mjou_058_183_198.pdf

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