THE POSITIVITY OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ASSOCIATED TO THE CHEREDNIK OPERATORS AND THE HECKMAN-OPDAM THEORY ATTACHED TO THE ROOT SYSTEMS OF TYPE B2 AND C2
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We consider the hypergeometric translation operator associated to the Cherednik operators and the Heckman-Opdam the- ory attached to the root system of type B2. We prove in this paper that these operators are positivity preserving and allow positive in- tegral representations. In particular we deduce that the product formulas of the Opdam-Cherednik and the Heckman-Opdam ker- nels are positive integral transforms, and we obtain best estimates of these kernels. The method used to obtain the previous results shows that these results are also true in the case of the root system of type C2.
Abstract
We consider the hypergeometric translation operator associated to the Cherednik operators and the Heckman-Opdam the- ory attached to the root system of type B2. We prove in this paper that these operators are positivity preserving and allow positive in- tegral representations. In particular we deduce that the product formulas of the Opdam-Cherednik and the Heckman-Opdam ker- nels are positive integral transforms, and we obtain best estimates of these kernels. The method used to obtain the previous results shows that these results are also true in the case of the root system of type C2.
참고문헌 (11)
- I. Cherednik, "A unification of Knizhnik-Zamslodchnikov equations and Dunkl operators via affine Hecke algebras", Invent. Math, 106, pp.411~432 (1990)
- G. J. Heckman, "Root systems and hypergeometric functions I", Compos Math, 64, pp.329~352 (1987)
- E. M. Opdam, "Harmonic analysis for certain representations of graded Hecke algebras", Acta Math, 175, pp.75~121 (1995)
- W. Rudin, "Real and complex analysis" (1974), McGraw-Hill Book Company
- B. Schapira, "Contribution to the hypergeometric function theory of Heckman and Opdam : sharp estimates, Schwartz spaces, heat kernel", Geom. Funct. Anal, 18, pp.222~250 (2008)
- K. Trimeche, "The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman-Opdam theory", Adv. Pure Appl. Math, 1, pp.293~323 (2010)
- K. Trimeche, "Harmonic analysis associated with the Cherednik operators and the Heckam-Opdam theory", Adv. Pure Appl. Math, 2, pp.23~46 (2011)
- K. Trimeche, "Hypergeometric convolution structure on LpLp-spaces and Applications, for the Heckman-Opdam theory", Preprint. Faculty of Sciences of Tunis, ~ (2012)
- K. Trimeche, "Positivity of the hypergeometric translation operators associated with the Cherednik operator, and of the Dunkl translation operators in the one dimentional case", Preprint. Faculty of Sciences of Tunis, ~ (2013)
- K. Trimeche, "The positivity of the hypergeometric translation operator and of its dual associated with the Cherednik operators and the Heckman-Opdam theory on RdRd", Preprint. Faculty of Sciences of Tunis, ~ (2013)
- K. Trimeche, "The positivity of the transmutation operators associated with the Cherednik operators attached to the root system of type B2B2 and C2C2", Preprint. Faculty of Sciences of Tunis, ~ (2014)