Metric Constrained Interpolation, Commutant Lifting and Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1998
|
| Schriftenreihe: | Operator Theory Advances and Applications
100 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book presents a unified approach for solving both stationary and nonstationary interpolation problems, in finite or infinite dimensions, based on the commutant lifting theorem from operator theory and the state space method from mathematical system theory. Initially the authors planned a number of papers treating nonstationary interpolation problems of Nevanlinna-Pick and Nehari type by reducing these nonstationary problems to stationary ones for operator-valued functions with operator arguments and using classical commutant lifting techniques. This reduction method required us to review and further develop the classical results for the stationary problems in this more general framework. Here the system theory turned out to be very useful for setting up the problems and for providing natural state space formulas for describing the solutions. In this way our work involved us in a much wider program than original planned. The final results of our efforts are presented here. The financial support in 1994 from the "NWO-stimulansprogramma" for the Thomas Stieltjes Institute for Mathematics in the Netherlands enabled us to start the research which lead to the present book. We also gratefully acknowledge the support from our home institutions: Indiana University at Bloomington, Purdue University at West Lafayette, Tel-Aviv University, and the Vrije Universiteit at Amsterdam. We warmly thank Dr. A.L. Sakhnovich for his carefully reading of a large part of the manuscript. Finally, Sharon Wise prepared very efficiently and with great care the troff file of this manuscript; we are grateful for her excellent typing |
| Beschreibung: | 1 Online-Ressource (XII, 587 p) |
| ISBN: | 9783034887915 9783034897754 |
| DOI: | 10.1007/978-3-0348-8791-5 |
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| 500 | |a This book presents a unified approach for solving both stationary and nonstationary interpolation problems, in finite or infinite dimensions, based on the commutant lifting theorem from operator theory and the state space method from mathematical system theory. Initially the authors planned a number of papers treating nonstationary interpolation problems of Nevanlinna-Pick and Nehari type by reducing these nonstationary problems to stationary ones for operator-valued functions with operator arguments and using classical commutant lifting techniques. This reduction method required us to review and further develop the classical results for the stationary problems in this more general framework. Here the system theory turned out to be very useful for setting up the problems and for providing natural state space formulas for describing the solutions. In this way our work involved us in a much wider program than original planned. The final results of our efforts are presented here. The financial support in 1994 from the "NWO-stimulansprogramma" for the Thomas Stieltjes Institute for Mathematics in the Netherlands enabled us to start the research which lead to the present book. We also gratefully acknowledge the support from our home institutions: Indiana University at Bloomington, Purdue University at West Lafayette, Tel-Aviv University, and the Vrije Universiteit at Amsterdam. We warmly thank Dr. A.L. Sakhnovich for his carefully reading of a large part of the manuscript. Finally, Sharon Wise prepared very efficiently and with great care the troff file of this manuscript; we are grateful for her excellent typing | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Foiaş, Ciprian 1933-2020 |
| author_GND | (DE-588)172077648 (DE-588)118915878 (DE-588)122738497 |
| author_facet | Foiaş, Ciprian 1933-2020 |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8791-5 |
| format | Electronic eBook |
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| id | DE-604.BV042422232 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034887915 9783034897754 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857649 |
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| physical | 1 Online-Ressource (XII, 587 p) |
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| publishDate | 1998 |
| publishDateSearch | 1998 |
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| series2 | Operator Theory Advances and Applications |
| spelling | Foiaş, Ciprian 1933-2020 Verfasser (DE-588)172077648 aut Metric Constrained Interpolation, Commutant Lifting and Systems by C. Foias, A. E. Frazho, I. Gohberg, M. A. Kaashoek Basel Birkhäuser Basel 1998 1 Online-Ressource (XII, 587 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory Advances and Applications 100 This book presents a unified approach for solving both stationary and nonstationary interpolation problems, in finite or infinite dimensions, based on the commutant lifting theorem from operator theory and the state space method from mathematical system theory. Initially the authors planned a number of papers treating nonstationary interpolation problems of Nevanlinna-Pick and Nehari type by reducing these nonstationary problems to stationary ones for operator-valued functions with operator arguments and using classical commutant lifting techniques. This reduction method required us to review and further develop the classical results for the stationary problems in this more general framework. Here the system theory turned out to be very useful for setting up the problems and for providing natural state space formulas for describing the solutions. In this way our work involved us in a much wider program than original planned. The final results of our efforts are presented here. The financial support in 1994 from the "NWO-stimulansprogramma" for the Thomas Stieltjes Institute for Mathematics in the Netherlands enabled us to start the research which lead to the present book. We also gratefully acknowledge the support from our home institutions: Indiana University at Bloomington, Purdue University at West Lafayette, Tel-Aviv University, and the Vrije Universiteit at Amsterdam. We warmly thank Dr. A.L. Sakhnovich for his carefully reading of a large part of the manuscript. Finally, Sharon Wise prepared very efficiently and with great care the troff file of this manuscript; we are grateful for her excellent typing Mathematics Mathematics, general Mathematik H-unendlich-Kontrolltheorie (DE-588)4488490-4 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Zeitinvariantes System (DE-588)4213493-6 gnd rswk-swf Liftungssatz (DE-588)4265072-0 gnd rswk-swf Kommutant (DE-588)4265073-2 gnd rswk-swf Zeitvariantes System (DE-588)4190654-8 gnd rswk-swf Zeitinvariantes System (DE-588)4213493-6 s Zeitvariantes System (DE-588)4190654-8 s Interpolation (DE-588)4162121-9 s Kommutant (DE-588)4265073-2 s Liftungssatz (DE-588)4265072-0 s H-unendlich-Kontrolltheorie (DE-588)4488490-4 s 1\p DE-604 Frazho, Arthur E. Sonstige oth Gohberg, Yiśrāʿēl Z. 1928-2009 Sonstige (DE-588)118915878 oth Kaashoek, Marinus A. 1937- Sonstige (DE-588)122738497 oth https://doi.org/10.1007/978-3-0348-8791-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Foiaş, Ciprian 1933-2020 Metric Constrained Interpolation, Commutant Lifting and Systems Mathematics Mathematics, general Mathematik H-unendlich-Kontrolltheorie (DE-588)4488490-4 gnd Interpolation (DE-588)4162121-9 gnd Zeitinvariantes System (DE-588)4213493-6 gnd Liftungssatz (DE-588)4265072-0 gnd Kommutant (DE-588)4265073-2 gnd Zeitvariantes System (DE-588)4190654-8 gnd |
| subject_GND | (DE-588)4488490-4 (DE-588)4162121-9 (DE-588)4213493-6 (DE-588)4265072-0 (DE-588)4265073-2 (DE-588)4190654-8 |
| title | Metric Constrained Interpolation, Commutant Lifting and Systems |
| title_auth | Metric Constrained Interpolation, Commutant Lifting and Systems |
| title_exact_search | Metric Constrained Interpolation, Commutant Lifting and Systems |
| title_full | Metric Constrained Interpolation, Commutant Lifting and Systems by C. Foias, A. E. Frazho, I. Gohberg, M. A. Kaashoek |
| title_fullStr | Metric Constrained Interpolation, Commutant Lifting and Systems by C. Foias, A. E. Frazho, I. Gohberg, M. A. Kaashoek |
| title_full_unstemmed | Metric Constrained Interpolation, Commutant Lifting and Systems by C. Foias, A. E. Frazho, I. Gohberg, M. A. Kaashoek |
| title_short | Metric Constrained Interpolation, Commutant Lifting and Systems |
| title_sort | metric constrained interpolation commutant lifting and systems |
| topic | Mathematics Mathematics, general Mathematik H-unendlich-Kontrolltheorie (DE-588)4488490-4 gnd Interpolation (DE-588)4162121-9 gnd Zeitinvariantes System (DE-588)4213493-6 gnd Liftungssatz (DE-588)4265072-0 gnd Kommutant (DE-588)4265073-2 gnd Zeitvariantes System (DE-588)4190654-8 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik H-unendlich-Kontrolltheorie Interpolation Zeitinvariantes System Liftungssatz Kommutant Zeitvariantes System |
| url | https://doi.org/10.1007/978-3-0348-8791-5 |
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