Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle

Orthogonal rational functions (ORF) on the unit circle generalize orthogonal polynomials (poles at infinity) and Laurent polynomials (poles at zero and infinity). In this paper we investigate the properties of and the relation between these ORF when the poles are all outside or all inside the unit d...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2017
Main Authors: Bultheel, A., Cruz-Barroso, R., Lasarow, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149239
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle / A. Bultheel, R. Cruz-Barroso, A. Lasarow // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 47 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:Orthogonal rational functions (ORF) on the unit circle generalize orthogonal polynomials (poles at infinity) and Laurent polynomials (poles at zero and infinity). In this paper we investigate the properties of and the relation between these ORF when the poles are all outside or all inside the unit disk, or when they can be anywhere in the extended complex plane outside the unit circle. Some properties of matrices that are the product of elementary unitary transformations will be proved and some connections with related algorithms for direct and inverse eigenvalue problems will be explained.
ISSN:1815-0659