Operator analysis: Hilbert space methods in complex analysis
This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Mode...
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| Hauptverfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom
Cambridge University Press
2020
|
| Schriftenreihe: | Cambridge tracts in mathematics
219 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 TUM01 TUM02 UBA01 UBW01 Volltext |
| Zusammenfassung: | This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 06 Mar 2020) The origins of operator-theoretic approaches to function theory -- Operator analysis on D : model formulas, lurking isometries, and positivity arguments -- Further development of models on the disc -- Operator analysis on D2 -- Carathéodory-Julia theory on the disc and the bidisc -- Herglotz and Nevanlinna representations in several variables -- Model theory on the symmetrized bidisc -- Spectral sets : three case studies -- Calcular norms -- Operator monotone functions -- Motivation for non-commutative functions -- Basic properties of non-commutative functions -- Montel theorems -- Free holomorphic functions -- The implicit function theorem -- Noncommutative functional calculus |
| Beschreibung: | 1 Online-Ressource (xv, 375 Seiten) |
| ISBN: | 9781108751292 |
| DOI: | 10.1017/9781108751292 |
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| 520 | |a This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices | ||
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Datensatz im Suchindex
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| author | Agler, Jim 1951- McCarthy, John E. 1964- Young, Nicholas 1943- |
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| author_facet | Agler, Jim 1951- McCarthy, John E. 1964- Young, Nicholas 1943- |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV046681133 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T14:24:06Z |
| indexdate | 2024-07-10T08:51:06Z |
| institution | BVB |
| isbn | 9781108751292 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032091947 |
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| physical | 1 Online-Ressource (xv, 375 Seiten) |
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| publishDate | 2020 |
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| publisher | Cambridge University Press |
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| spelling | Agler, Jim 1951- (DE-588)1185705627 aut Operator analysis Hilbert space methods in complex analysis Jim Agler, John Edward McCarthy, Nicholas Young Cambridge, United Kingdom Cambridge University Press 2020 1 Online-Ressource (xv, 375 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 219 Title from publisher's bibliographic system (viewed on 06 Mar 2020) The origins of operator-theoretic approaches to function theory -- Operator analysis on D : model formulas, lurking isometries, and positivity arguments -- Further development of models on the disc -- Operator analysis on D2 -- Carathéodory-Julia theory on the disc and the bidisc -- Herglotz and Nevanlinna representations in several variables -- Model theory on the symmetrized bidisc -- Spectral sets : three case studies -- Calcular norms -- Operator monotone functions -- Motivation for non-commutative functions -- Basic properties of non-commutative functions -- Montel theorems -- Free holomorphic functions -- The implicit function theorem -- Noncommutative functional calculus This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices Operator theory Holomorphic functions Geometric function theory Hilbert space Geometrische Funktionentheorie (DE-588)4156711-0 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s Geometrische Funktionentheorie (DE-588)4156711-0 s DE-604 McCarthy, John E. 1964- (DE-588)1056135700 aut Young, Nicholas 1943- (DE-588)1185709320 aut Erscheint auch als Druck-Ausgabe 978-1-10848-544-9 Cambridge tracts in mathematics 219 (DE-604)BV047362617 219 https://doi.org/10.1017/9781108751292 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Agler, Jim 1951- McCarthy, John E. 1964- Young, Nicholas 1943- Operator analysis Hilbert space methods in complex analysis Cambridge tracts in mathematics Operator theory Holomorphic functions Geometric function theory Hilbert space Geometrische Funktionentheorie (DE-588)4156711-0 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4156711-0 (DE-588)4075665-8 |
| title | Operator analysis Hilbert space methods in complex analysis |
| title_auth | Operator analysis Hilbert space methods in complex analysis |
| title_exact_search | Operator analysis Hilbert space methods in complex analysis |
| title_exact_search_txtP | Operator analysis Hilbert space methods in complex analysis |
| title_full | Operator analysis Hilbert space methods in complex analysis Jim Agler, John Edward McCarthy, Nicholas Young |
| title_fullStr | Operator analysis Hilbert space methods in complex analysis Jim Agler, John Edward McCarthy, Nicholas Young |
| title_full_unstemmed | Operator analysis Hilbert space methods in complex analysis Jim Agler, John Edward McCarthy, Nicholas Young |
| title_short | Operator analysis |
| title_sort | operator analysis hilbert space methods in complex analysis |
| title_sub | Hilbert space methods in complex analysis |
| topic | Operator theory Holomorphic functions Geometric function theory Hilbert space Geometrische Funktionentheorie (DE-588)4156711-0 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Operator theory Holomorphic functions Geometric function theory Hilbert space Geometrische Funktionentheorie Operatortheorie |
| url | https://doi.org/10.1017/9781108751292 |
| volume_link | (DE-604)BV047362617 |
| work_keys_str_mv | AT aglerjim operatoranalysishilbertspacemethodsincomplexanalysis AT mccarthyjohne operatoranalysishilbertspacemethodsincomplexanalysis AT youngnicholas operatoranalysishilbertspacemethodsincomplexanalysis |