A right inverse of the Askey-Wilson operator

1993/10/05 by B. M. Brown, B. Malcolm Brown, Mourad E. H. Ismail +2 · 1 citation
Mathematics · #Differential Equations and Boundary Problems #Holomorphic and Operator Theory #Mathematical functions and polynomials #math.CA

paper · pdf · doi:10.48550/arxiv.math/9310219

arxiv created 1993/10/05 · arxiv updated 2009/11/30

Abstract

We establish an integral representation of a right inverse of the Askey-Wilson finite difference operator on L² with weight (1-x²)^-1/2. The kernel of this integral operator is ϑ'₄/ϑ₄ and is the Riemann mapping function that maps the open unit disc conformally onto the interior of an ellipse.

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