Diagonalization of certain integral operators II
Mourad E. H. Ismail, Mizan Rahman, Ruiming Zhang
Abstract
We establish an integral representations of a right inverses of the Askey-Wilson finite difference operator in an L2 space weighted by the weight function of the continuous q-Jacobi polynomials. We characterize the eigenvalues of this integral operator and prove a q-analog of the expansion of eixy in Jacobi polynomials of argument x. We also outline a general procedure of finding integral representations for inverses of linear operators.
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