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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2017 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2017
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149239 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862546090091347968 |
|---|---|
| author | Bultheel, A. Cruz-Barroso, R. Lasarow, A. |
| author_facet | Bultheel, A. Cruz-Barroso, R. Lasarow, A. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2025-11-25T10:21:02Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149239 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T10:21:02Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bultheel, A. Cruz-Barroso, R. Lasarow, A. 2019-02-19T19:12:39Z 2019-02-19T19:12:39Z 2017 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. 1815-0659 2010 Mathematics Subject Classification: 30D15; 30E05; 42C05; 44A60 DOI:10.3842/SIGMA.2017.090 https://nasplib.isofts.kiev.ua/handle/123456789/149239 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle Article published earlier |
| spellingShingle | Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle Bultheel, A. Cruz-Barroso, R. Lasarow, A. |
| title | Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle |
| title_full | Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle |
| title_fullStr | Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle |
| title_full_unstemmed | Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle |
| title_short | Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle |
| title_sort | orthogonal rational functions on the unit circle with prescribed poles not on the unit circle |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149239 |
| work_keys_str_mv | AT bultheela orthogonalrationalfunctionsontheunitcirclewithprescribedpolesnotontheunitcircle AT cruzbarrosor orthogonalrationalfunctionsontheunitcirclewithprescribedpolesnotontheunitcircle AT lasarowa orthogonalrationalfunctionsontheunitcirclewithprescribedpolesnotontheunitcircle |