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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.
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참고문헌 (12)
참고문헌 신청
I. Cherednik / 1997 / Inverse Harish-Chandra transform and difference operators / Internat. Math. Res. Notices 15:733~750
L. Gallardo / 2012 / Positivity of the Jacobi-Cherednik intertwining operator and its dual / Adv. Pure Appl. Math 1:163~194
G. J. Heckman / 1987 / Root systems and hypergeometric functions I / Compositio Math 64:329~352
T. H. Koornwinder / 1975 / A new proof of the Paley-Wiener type theorem for the Jacobi transform / Arkiv For Math 13(1):145~159
T.H.Koornwinder / 1993 / Wavelets: An elementary treatment of theory and applications / World Scientific :27~48
L. Gallardo / 2012 / Positivity of the Jacobi-Cherednik intertwining operator and its dual / Adv. Pure Appl. Math 1:163~194
G. J. Heckman / 1987 / Root systems and hypergeometric functions I / Compositio Math 64:329~352
T. H. Koornwinder / 1975 / A new proof of the Paley-Wiener type theorem for the Jacobi transform / Arkiv For Math 13(1):145~159
T.H.Koornwinder / 1993 / Wavelets: An elementary treatment of theory and applications / World Scientific :27~48
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