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