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Ladder operators for Szego polynomials and related biorthogonal rational functions

Authors: Mourad E. H. Ismail and Mizan Rahman
Journal: Proc. Amer. Math. Soc. 124 (1996), 2149-2159
MSC (1991): Primary 33D45; Secondary 30E05
MathSciNet review: 1350949
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Abstract: We find the raising and lowering operators for orthogonal polynomials on the unit circle introduced by Szego and for their four parameter generalization to ${}_4\phi _3$ biorthogonal rational functions on the unit circle.

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Additional Information

Mourad E. H. Ismail
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620

Mizan Rahman
Affiliation: Department of Mathematics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

Keywords: Szeg\H{o} polynomials, $q$-difference operators, orthogonality on the unit circle, $q$-beta integrals, biorthogonal rational functions, raising and lowering operators, $q$-Sturm-Liouville equations.
Received by editor(s): July 5, 1994
Received by editor(s) in revised form: February 2, 1995
Additional Notes: Research partially supported by NSF grant DMS 9203659 and NSERC grant A6197
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society