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The Askey–Wilson polynomials and q-Sturm–Liouville problems*

Published online by Cambridge University Press:  24 October 2008

B. Malcolm Brown ,
W. Desmond Evans  and
Mourad E. H. Ismail
B. Malcolm Brown
Affiliation:
Department of Computing Mathematics, University of Wales College at CardiffCardiff, Wales CF2 4YN
W. Desmond Evans
Affiliation:
School of Mathematics, University of Wales College at Cardiff, Cardiff, Wales CF4 2YN
Mourad E. H. Ismail
Affiliation:
Department of Mathematics, University of South Florida, Tampa, FL 33620, U.S.A.
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Abstract

We find the adjoint of the Askey–Wilson divided difference operator with respect to the inner product on L2(–1, 1, (1– x2)½dx) defined as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm–Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic description of the Askey-Wilson operator.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 1 , January 1996 , pp. 1 - 16
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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