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Proceedings of the American Mathematical Society

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A right inverse of the Askey-Wilson operator


Authors: B. Malcolm Brown and Mourad E. H. Ismail
Journal: Proc. Amer. Math. Soc. 123 (1995), 2071-2079
MSC: Primary 33D20; Secondary 33D45, 39A70, 42C10, 45E10
DOI: https://doi.org/10.1090/S0002-9939-1995-1273478-X
MathSciNet review: 1273478
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1273478-X
Keywords: Integral operator, Chebyshev polynomials, theta functions, finite difference operators, conformal mappings, q-Hermite polynomials
Article copyright: © Copyright 1995 American Mathematical Society