Schur Parameters, Factorization and Dilation Problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1996
|
| Schriftenreihe: | Operator Theory Advances and Applications
82 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The subject of this book is about the ubiquity of the Schur parameters, whose introduction goes back to a paper of I. Schur in 1917 concerning an interpolation problem of C. Caratheodory. What followed there appears to be a truly fascinating story which, however, should be told by a professional historian. Here we provide the reader with a simplified version, mostly related to the contents of the book. In the twenties, thf~ theory of orthogonal polynomials on the unit circle was developed by G. Szego and the formulae relating these polynomials involved num bers (usually called Szego parameters) similar to the Schur parameters. Mean while, R. Nevanlinna and G. Pick studied the theory of another interpolation problem, known since then as the Nevanlinna-Pick problem, and an algorithm similar to Schur's one was obtained by Nevanlinna. In 1957, Z. Nehari solved OO an L problem which contained both Caratheodory-Schur and Nevannlina-Pick problems as particular cases. Apparently unrelated work of H. Weyl, J. von Neu mann and K. Friedericks concerning selfadjoint extensions of symmetric operators was connected to interpolation by M. A. Naimark and M. G Krein using some gen eral dilation theoretic ideas. Classical moment problems, like the trigonometric moment and Hamburger moment problems, were also related to these topics and a comprehensive account of what can be called the classical period has appeared in the monograph of M. G. Krein and A. A. Nudelman, [KN] |
| Beschreibung: | 1 Online-Ressource (X, 254 p) |
| ISBN: | 9783034891080 9783034899109 |
| DOI: | 10.1007/978-3-0348-9108-0 |
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Datensatz im Suchindex
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| discipline | Mathematik |
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| spelling | Constantinescu, Tiberiu Verfasser aut Schur Parameters, Factorization and Dilation Problems by Tiberiu Constantinescu Basel Birkhäuser Basel 1996 1 Online-Ressource (X, 254 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory Advances and Applications 82 The subject of this book is about the ubiquity of the Schur parameters, whose introduction goes back to a paper of I. Schur in 1917 concerning an interpolation problem of C. Caratheodory. What followed there appears to be a truly fascinating story which, however, should be told by a professional historian. Here we provide the reader with a simplified version, mostly related to the contents of the book. In the twenties, thf~ theory of orthogonal polynomials on the unit circle was developed by G. Szego and the formulae relating these polynomials involved num bers (usually called Szego parameters) similar to the Schur parameters. Mean while, R. Nevanlinna and G. Pick studied the theory of another interpolation problem, known since then as the Nevanlinna-Pick problem, and an algorithm similar to Schur's one was obtained by Nevanlinna. In 1957, Z. Nehari solved OO an L problem which contained both Caratheodory-Schur and Nevannlina-Pick problems as particular cases. Apparently unrelated work of H. Weyl, J. von Neu mann and K. Friedericks concerning selfadjoint extensions of symmetric operators was connected to interpolation by M. A. Naimark and M. G Krein using some gen eral dilation theoretic ideas. Classical moment problems, like the trigonometric moment and Hamburger moment problems, were also related to these topics and a comprehensive account of what can be called the classical period has appeared in the monograph of M. G. Krein and A. A. Nudelman, [KN] Mathematics Mathematics, general Mathematik Operatortheorie (DE-588)4075665-8 gnd rswk-swf Faktorisierung (DE-588)4128927-4 gnd rswk-swf Fortsetzung Mathematik (DE-588)4334458-6 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Dilatation (DE-588)4149923-2 gnd rswk-swf Normierter Raum (DE-588)4127735-1 gnd rswk-swf Schur-Parameter (DE-588)4432315-3 gnd rswk-swf Normierter Raum (DE-588)4127735-1 s Interpolation (DE-588)4162121-9 s Schur-Parameter (DE-588)4432315-3 s 1\p DE-604 Dilatation (DE-588)4149923-2 s Operatortheorie (DE-588)4075665-8 s Faktorisierung (DE-588)4128927-4 s 2\p DE-604 3\p DE-604 Fortsetzung Mathematik (DE-588)4334458-6 s 4\p DE-604 https://doi.org/10.1007/978-3-0348-9108-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Constantinescu, Tiberiu Schur Parameters, Factorization and Dilation Problems Mathematics Mathematics, general Mathematik Operatortheorie (DE-588)4075665-8 gnd Faktorisierung (DE-588)4128927-4 gnd Fortsetzung Mathematik (DE-588)4334458-6 gnd Interpolation (DE-588)4162121-9 gnd Dilatation (DE-588)4149923-2 gnd Normierter Raum (DE-588)4127735-1 gnd Schur-Parameter (DE-588)4432315-3 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4128927-4 (DE-588)4334458-6 (DE-588)4162121-9 (DE-588)4149923-2 (DE-588)4127735-1 (DE-588)4432315-3 |
| title | Schur Parameters, Factorization and Dilation Problems |
| title_auth | Schur Parameters, Factorization and Dilation Problems |
| title_exact_search | Schur Parameters, Factorization and Dilation Problems |
| title_full | Schur Parameters, Factorization and Dilation Problems by Tiberiu Constantinescu |
| title_fullStr | Schur Parameters, Factorization and Dilation Problems by Tiberiu Constantinescu |
| title_full_unstemmed | Schur Parameters, Factorization and Dilation Problems by Tiberiu Constantinescu |
| title_short | Schur Parameters, Factorization and Dilation Problems |
| title_sort | schur parameters factorization and dilation problems |
| topic | Mathematics Mathematics, general Mathematik Operatortheorie (DE-588)4075665-8 gnd Faktorisierung (DE-588)4128927-4 gnd Fortsetzung Mathematik (DE-588)4334458-6 gnd Interpolation (DE-588)4162121-9 gnd Dilatation (DE-588)4149923-2 gnd Normierter Raum (DE-588)4127735-1 gnd Schur-Parameter (DE-588)4432315-3 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Operatortheorie Faktorisierung Fortsetzung Mathematik Interpolation Dilatation Normierter Raum Schur-Parameter |
| url | https://doi.org/10.1007/978-3-0348-9108-0 |
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