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Spectral theorems associated with the Jacobi–Cherednik operator
Journal article   Open access  Peer reviewed

Spectral theorems associated with the Jacobi–Cherednik operator

Hatem Mejjaoli
Bulletin des sciences mathématiques, Vol.138(3), pp.416-439
01/04/2014
DOI: https://doi.org/10.1016/j.bulsci.2013.10.004

Abstract

Jacobi–Cherednik operator Opdam–Cherednik transform Real Paley–Wiener theorems
In this paper, we establish real Paley–Wiener theorems for the Opdam–Cherednik transform on R. More precisely, we characterize the functions in the generalized Schwartz space Sk,k′r(R) and in LAk,k′p(R) whose Opdam–Cherednik transform has bounded, unbounded, convex and nonconvex support. Finally we study the spectral problems on the generalized tempered distributions Sk,k′′2(R).
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https://doi.org/10.1016/j.bulsci.2013.10.004View
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