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The Askey-Wilson polynomials and q-Sturm-Lioville problems

B. Malcolm Brown·William Desmond Evans·Mourad E. H. Ismail
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Abstract

We find the adjoint of the Askey-Wilson divided difference operator with respect to the inner procuct on L^2(-1,1,(1-x^2)^-1/2 dx) defined as a Cauchy principle 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.

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B. Malcolm Brown, William Desmond Evans, Mourad E. H. Ismail. 1994-08-24. The Askey-Wilson polynomials and q-Sturm-Lioville problems. https://arxiv.org/abs/math/9408209

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