The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman--Opdam theory on ℝ^d

References

[1] Cherednik I., A unification of Knizhnik–Zamslodchnikov equations and Dunkl operators via affine Hecke algebras, Invent. Math. 106 (1990), 411–432. 10.1007/BF01243918Search in Google Scholar

[2] Heckman G. J. and Opdam E. M., Root systems and hypergeometric functions I, Compos. Math. 64 (1987), 329–352. Search in Google Scholar

[3] Opdam E. M., Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995), 75–121. 10.1007/BF02392487Search in Google Scholar

[4] Rudin W., Real and Complex Analysis, 2nd ed., McGraw–Hill, New York, 1974. Search in Google Scholar

[5] Schapira B., Contribution to the hypergeometric function theory of Heckman and Opdam: Sharp estimates, Schwartz spaces, heat kernel, Geom. Funct. Anal. 18 (2008), 222–250. 10.1007/s00039-008-0658-7Search in Google Scholar

[6] Trimèche K., The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory, Adv. Pure Appl. Math. 1 (2010), 293–323. 10.1515/apam.2010.015Search in Google Scholar

[7] Trimèche K., Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory, Adv. Pure Appl. Math. 2 (2011), 23–46. 10.1515/apam.2011.022Search in Google Scholar

[8] Trimèche K., The Harmonic Analysis Associated to the Heckman–Opdam Theory and Its Application to a Some Root System Of Type B⁢Cd, Faculty of Sciences of Tunis, Tunis, 2015. Search in Google Scholar

[9] Trimèche K., Positivity of the transmutation operators and absolute continuity of their representing measures for a root system on ℝd, Int. J. Appl. Math. 28 (2015), no. 4, 427–453. Search in Google Scholar