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

被引：23

作者：

Brown, BM

Evans, WD

Ismail, MEH

机构：

[1] UNIV WALES COLL CARDIFF,SCH MATH,CARDIFF CF4 2YN,S GLAM,WALES

[2] UNIV S FLORIDA,DEPT MATH,TAMPA,FL 33620

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 1996年 / 119卷

关键词：

D O I：

10.1017/S0305004100073916

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find the adjoint of the Askey-Wilson divided difference operator with respect to the inner product on L(2)(-1, 1, (1-x(2))(-1/2)dx) 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.

引用

页码：1 / 16

页数：16

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