The Cherednik and the Gaussian Cherednik Windowed transforms on $\mathbb{R}^d$ in the W-invariant case
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper we give the harmonic analysis associated with the Cherednik operators, next we define and study the Cherednik wavelets and the Cherednik windowed transforms on $\mathbb{R}^d$, in the W-invariant case, and we prove for these transforms Plancherel and inversion formulas. As application we give these results for the Gaussian Cherednik wavelets and the Gaussian Cherednik windowed transform on $\mathbb{R}^d$ in the W-invariant case.
Abstract
In this paper we give the harmonic analysis associated with the Cherednik operators, next we define and study the Cherednik wavelets and the Cherednik windowed transforms on $\mathbb{R}^d$, in the W-invariant case, and we prove for these transforms Plancherel and inversion formulas. As application we give these results for the Gaussian Cherednik wavelets and the Gaussian Cherednik windowed transform on $\mathbb{R}^d$ in the W-invariant case.
참고문헌 (12)
- I. Cherednik, "Inverse Harish-Chandra transform and difference operators", Internat. Math. Res. Notices, 15, pp.733~750 (1997)
- L. Gallardo, "Positivity of the Jacobi-Cherednik intertwining operator and its dual", Adv. Pure Appl. Math, 1, pp.163~194 (2012)
- G. J. Heckman, "Root systems and hypergeometric functions I", Compositio Math, 64, pp.329~352 (1987)
- T. H. Koornwinder, "A new proof of the Paley-Wiener type theorem for the Jacobi transform", Arkiv For Math, 13(1), pp.145~159 (1975)
- T.H.Koornwinder, "Wavelets: An elementary treatment of theory and applications", pp.27~48 (1993), World Scientific
- E. M. Opdam, "Harmonic analysis for certain representations of graded Hecke algebras", Acta Math, 175, pp.75~121 (1995)
- B.Schapira, "Etude analytique et probabiliste de Laplacians associ´es `a des syst`emes de racines: Laplacian hyperg´eom´etrique de Heckman-Opdam et Laplacian combinatoire sur les immeubles affines", Ph. D., pp.2006
- 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, "Generalized Wavelets and Hypergroups" (1997), Gordon and Breach Science Publishers
- K. Trimeche, "The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operator 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 Heckman-Opdam theory", Adv. Pure Appl. Math, 2, pp.23~46 (2011)
- Khalifa Trimeche, "The harmonic analysis associated to the Heckman-Opdam's theory and its application to a root system of type $BC_d$", 한국수학논문집, 27(1), pp.221~267 (2019), 강원경기수학회