Noncommutative function-theoretic operator theory and applications:
This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and repr...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2021
|
| Series: | Cambridge tracts in mathematics
225 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling-Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges-Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings |
| Item Description: | Title from publisher's bibliographic system (viewed on 09 Dec 2021) |
| Physical Description: | 1 Online-Ressource (x, 428 Seiten) |
| ISBN: | 9781009004305 |
| DOI: | 10.1017/9781009004305 |
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| id | DE-604.BV047707969 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:59:46Z |
| indexdate | 2024-07-10T09:19:44Z |
| institution | BVB |
| isbn | 9781009004305 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033091808 |
| oclc_num | 1294755979 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 Online-Ressource (x, 428 Seiten) |
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| publishDate | 2021 |
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| publisher | Cambridge University Press |
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| series2 | Cambridge tracts in mathematics 225 |
| spelling | Ball, Joseph A. 1947- (DE-588)112083498 aut Noncommutative function-theoretic operator theory and applications Joseph A. Ball, Vladimir Bolotnikov Cambridge Cambridge University Press 2021 1 Online-Ressource (x, 428 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 225 Title from publisher's bibliographic system (viewed on 09 Dec 2021) This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling-Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges-Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings Hardy spaces Functions of complex variables Bolotnikov, Vladimir 1962- (DE-588)131720236 aut Erscheint auch als Druck-Ausgabe 978-1-31-651899-1 https://doi.org/10.1017/9781009004305 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Ball, Joseph A. 1947- Bolotnikov, Vladimir 1962- Noncommutative function-theoretic operator theory and applications Hardy spaces Functions of complex variables |
| title | Noncommutative function-theoretic operator theory and applications |
| title_auth | Noncommutative function-theoretic operator theory and applications |
| title_exact_search | Noncommutative function-theoretic operator theory and applications |
| title_exact_search_txtP | Noncommutative function-theoretic operator theory and applications |
| title_full | Noncommutative function-theoretic operator theory and applications Joseph A. Ball, Vladimir Bolotnikov |
| title_fullStr | Noncommutative function-theoretic operator theory and applications Joseph A. Ball, Vladimir Bolotnikov |
| title_full_unstemmed | Noncommutative function-theoretic operator theory and applications Joseph A. Ball, Vladimir Bolotnikov |
| title_short | Noncommutative function-theoretic operator theory and applications |
| title_sort | noncommutative function theoretic operator theory and applications |
| topic | Hardy spaces Functions of complex variables |
| topic_facet | Hardy spaces Functions of complex variables |
| url | https://doi.org/10.1017/9781009004305 |
| work_keys_str_mv | AT balljosepha noncommutativefunctiontheoreticoperatortheoryandapplications AT bolotnikovvladimir noncommutativefunctiontheoreticoperatortheoryandapplications |