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Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle
Інший ID:
2010 Mathematics Subject Classification: 30D15; 30E05; 42C05; 44A60
DOI:10.3842/SIGMA.2017.090
DOI:10.3842/SIGMA.2017.090
Посилання:
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.
Підтримка:
This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14). The full collection is available at https://www.emis.de/journals/SIGMA/OPSFA2017.html.
We thank the anonymous referees for their careful reading of the manuscript and their suggestions for improvement.
Дата:
2017
Переглядів:
640
Завантажень:
263
Анотація:
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.
