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

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

© 2017, Institute of Mathematics. All rights reserved. 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...

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Veröffentlicht in:SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 2017-01, Vol.13
Hauptverfasser: Bultheel, Adhemar, Cruz Barroso, R, Lasarow, Andreas
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Cruz Barroso, R
Lasarow, Andreas
description © 2017, Institute of Mathematics. All rights reserved. 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.
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All rights reserved. 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. 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All rights reserved. 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.</abstract><pub>NATL ACAD SCI UKRAINE, INST MATH</pub><oa>free_for_read</oa></addata></record>
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title Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle
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