A right inverse of the Askey-Wilson operator

Brown, B. Malcolm; Ismail, Mourad E. H.

doi:10.1090/S0002-9939-1995-1273478-X

A right inverse of the Askey-Wilson operator
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by B. Malcolm Brown and Mourad E. H. Ismail

Proc. Amer. Math. Soc. 123 (1995), 2071-2079

DOI: https://doi.org/10.1090/S0002-9939-1995-1273478-X

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Abstract:

We establish an integral representation of a right inverse of the Askey-Wilson finite difference operator on ${L^2}$ with weight ${(1 - {x^2})^{ - 1/2}}$. The kernel of this integral operator is $\vartheta _4’/\vartheta _4$ and is the Riemann mapping function that maps the interior of an ellipse conformally onto the open unit disc.

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