Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1997
|
| Schriftenreihe: | Operator Theory Advances and Applications
96 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case |
| Beschreibung: | 1 Online-Ressource (XI, 232 p) |
| ISBN: | 9783034889087 9783034898232 |
| DOI: | 10.1007/978-3-0348-8908-7 |
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| 264 | 1 | |a Basel |b Birkhäuser Basel |c 1997 | |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034889087 9783034898232 |
| language | English |
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| spelling | Alpay, Daniel Verfasser aut Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces by Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik Snoo Basel Birkhäuser Basel 1997 1 Online-Ressource (XI, 232 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory Advances and Applications 96 Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case Mathematics Engineering Mathematics, general Engineering, general Ingenieurwissenschaften Mathematik Schur-Funktion (DE-588)4180243-3 gnd rswk-swf Pontrjagin-Raum (DE-588)4473351-3 gnd rswk-swf Operator colligation (DE-588)4473350-1 gnd rswk-swf Schur-Funktion (DE-588)4180243-3 s Operator colligation (DE-588)4473350-1 s Pontrjagin-Raum (DE-588)4473351-3 s 1\p DE-604 Dijksma, Aad Sonstige oth Rovnyak, James Sonstige oth Snoo, Hendrik Sonstige oth https://doi.org/10.1007/978-3-0348-8908-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Alpay, Daniel Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces Mathematics Engineering Mathematics, general Engineering, general Ingenieurwissenschaften Mathematik Schur-Funktion (DE-588)4180243-3 gnd Pontrjagin-Raum (DE-588)4473351-3 gnd Operator colligation (DE-588)4473350-1 gnd |
| subject_GND | (DE-588)4180243-3 (DE-588)4473351-3 (DE-588)4473350-1 |
| title | Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces |
| title_auth | Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces |
| title_exact_search | Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces |
| title_full | Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces by Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik Snoo |
| title_fullStr | Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces by Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik Snoo |
| title_full_unstemmed | Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces by Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik Snoo |
| title_short | Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces |
| title_sort | schur functions operator colligations and reproducing kernel pontryagin spaces |
| topic | Mathematics Engineering Mathematics, general Engineering, general Ingenieurwissenschaften Mathematik Schur-Funktion (DE-588)4180243-3 gnd Pontrjagin-Raum (DE-588)4473351-3 gnd Operator colligation (DE-588)4473350-1 gnd |
| topic_facet | Mathematics Engineering Mathematics, general Engineering, general Ingenieurwissenschaften Mathematik Schur-Funktion Pontrjagin-Raum Operator colligation |
| url | https://doi.org/10.1007/978-3-0348-8908-7 |
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