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http://dx.doi.org/10.11568/kjm.2020.28.4.649

THE CHEREDNIK AND THE GAUSSIAN CHEREDNIK WINDOWED TRANSFORMS ON ℝd IN THE W-INVARIANT CASE  

Hassini, Amina (Faculty of Sciences of tunis, Department of Mathematics)
Trimeche, Khalifa (Faculty of Sciences of tunis, Department of Mathematics)
Publication Information
Korean Journal of Mathematics / v.28, no.4, 2020 , pp. 649-671 More about this Journal
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 ℝd, 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 ℝd in the W-invariant case.
Keywords
Cherednik wavelets; Cherednik operators; Cherednik windowed transform; Gaussian Cherednik Wavelets; Gaussian Cherednik windowed transform;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 T.H.Koornwinder, The continuous wavelet transform. Series in Approximations and Decompositions. Vol. 1. Wavelets: An elementary treatment of theory and applications. Edited by T.H.Koornwinder, World Scientific, (1993), 27-48.
2 E.M.Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995), 75-121.   DOI
3 B.Schapira, Etude analytique et probabiliste de Laplacians associes a des systemes de racines: Laplacian hypergeometrique de Heckman-Opdam et Laplacian combinatoire sur les immeubles affines, Ph. D. Thesis, University of Orleans, 2006.
4 B.Schapira, Contribution to the hypergeometric function theory of Heckman and Opdam; sharp estimates, Schwartz spaces, heat kernel, Geom. Funct. Anal. 18 (2008), 222-250.   DOI
5 K.Trimeche, Generalized Wavelets and Hypergroups, Gordon and Breach Science Publishers, 1997.
6 G.J.Heckman and E.M.Opdam, Root systems and hypergeometric functions I, Compositio Math. 64 (1987), 329-352.
7 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 (2010), 293-323.   DOI
8 I.Cherednik, Inverse Harish-Chandra transform and difference operators, Internat. Math. Res. Notices 15 (1997), 733-750.   DOI
9 L.Gallardo and K.Trimeche, Positivity of the Jacobi-Cherednik intertwining operator and its dual, Adv. Pure Appl. Math. 1 (2012), 163-194.   DOI
10 T.H.Koornwinder, A new proof of the Paley-Wiener type theorem for the Jacobi transform, Arkiv For Math. 13 (1) (1975), 145-159.   DOI
11 K.Trimeche, Harmonic analysis associated with the Cherednik operators and the Heckman-Opdam theory, Adv. Pure Appl. Math. 2 (2011), 23-46.   DOI
12 K.Trimeche, The harmonic analysis associated to the Heckman-Opdam theory and its applications to the root system of type BCd, Korean J. Math. 27 (2019) (1), 221-267.   DOI