Diagonalization of certain integral operators II

1993/10/05 by Mourad E. H. Ismail, Mizan Rahman, Ismail, Mourad E. H. +3
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.math/9310221

openalex publication_date 1993/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 e^ixy in Jacobi polynomials of argument x. We also outline a general procedure of finding integral representations for inverses of linear operators.

Related

• A right inverse of the Askey-Wilson operator
• q-Fractional Integral Operators With Two Parameters
• Jacobi operator, q-difference equation and orthogonal polynomials
• Dual forms of the orthogonality relations of some classical q-orthogonal polynomials
• q-special functions, basic hypergeometric series and operators