Spectral theorems associated with the Jacobi–Cherednik operator

In this paper, we establish real Paley–Wiener theorems for the Opdam–Cherednik transform on RR. 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).