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

DOI:
https://doi.org/10.1090/S0002-9939-96-03304-7

MathSciNet review:
1350949

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Abstract | References | Similar Articles | Additional Information

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 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

DOI:
https://doi.org/10.1090/S0002-9939-96-03304-7

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