A primer on the Dirichlet space:
The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic acc...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2014
|
| Schriftenreihe: | Cambridge tracts in mathematics
203 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students |
| Beschreibung: | 1 Online-Ressource (xiii, 211 Seiten) |
| ISBN: | 9781107239425 |
| DOI: | 10.1017/CBO9781107239425 |
Internformat
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| 245 | 1 | 0 | |a A primer on the Dirichlet space |c Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford |
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| 300 | |a 1 Online-Ressource (xiii, 211 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge tracts in mathematics |v 203 | |
| 505 | 8 | |a Preface -- Basic notions -- Capacity -- Boundary behavior -- Zero sets -- Multipliers -- Conformal invariance -- Harmonically weighted Dirichlet spaces -- Invariant subspaces -- Cyclicity -- Appendix A. Hardy spaces -- Appendix B. The Hardy-Littlewood maximal function -- Appendix C. Positive definite matrices -- Appendix D. Regularization and the rising-sun lemma | |
| 520 | |a The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students | ||
| 650 | 4 | |a Dirichlet principle | |
| 650 | 4 | |a Hilbert space | |
| 650 | 4 | |a Holomorphic functions | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 0 | 7 | |a Dirichlet-Raum |0 (DE-588)4621988-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804176883453001728 |
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| any_adam_object | |
| author | El-Fallah, Omar |
| author_GND | (DE-588)1073324729 |
| author_facet | El-Fallah, Omar |
| author_role | aut |
| author_sort | El-Fallah, Omar |
| author_variant | o e f oef |
| building | Verbundindex |
| bvnumber | BV043941555 |
| classification_rvk | SK 750 |
| collection | ZDB-20-CBO |
| contents | Preface -- Basic notions -- Capacity -- Boundary behavior -- Zero sets -- Multipliers -- Conformal invariance -- Harmonically weighted Dirichlet spaces -- Invariant subspaces -- Cyclicity -- Appendix A. Hardy spaces -- Appendix B. The Hardy-Littlewood maximal function -- Appendix C. Positive definite matrices -- Appendix D. Regularization and the rising-sun lemma |
| ctrlnum | (ZDB-20-CBO)CR9781107239425 (OCoLC)894732681 (DE-599)BVBBV043941555 |
| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107239425 |
| format | Electronic eBook |
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| id | DE-604.BV043941555 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:15Z |
| institution | BVB |
| isbn | 9781107239425 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350525 |
| oclc_num | 894732681 |
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| physical | 1 Online-Ressource (xiii, 211 Seiten) |
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| publishDate | 2014 |
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| publisher | Cambridge University Press |
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| spelling | El-Fallah, Omar Verfasser (DE-588)1073324729 aut A primer on the Dirichlet space Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford Cambridge Cambridge University Press 2014 1 Online-Ressource (xiii, 211 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 203 Preface -- Basic notions -- Capacity -- Boundary behavior -- Zero sets -- Multipliers -- Conformal invariance -- Harmonically weighted Dirichlet spaces -- Invariant subspaces -- Cyclicity -- Appendix A. Hardy spaces -- Appendix B. The Hardy-Littlewood maximal function -- Appendix C. Positive definite matrices -- Appendix D. Regularization and the rising-sun lemma The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students Dirichlet principle Hilbert space Holomorphic functions Functions of complex variables Dirichlet-Raum (DE-588)4621988-2 gnd rswk-swf Dirichlet-Raum (DE-588)4621988-2 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-04752-5 https://doi.org/10.1017/CBO9781107239425 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | El-Fallah, Omar A primer on the Dirichlet space Preface -- Basic notions -- Capacity -- Boundary behavior -- Zero sets -- Multipliers -- Conformal invariance -- Harmonically weighted Dirichlet spaces -- Invariant subspaces -- Cyclicity -- Appendix A. Hardy spaces -- Appendix B. The Hardy-Littlewood maximal function -- Appendix C. Positive definite matrices -- Appendix D. Regularization and the rising-sun lemma Dirichlet principle Hilbert space Holomorphic functions Functions of complex variables Dirichlet-Raum (DE-588)4621988-2 gnd |
| subject_GND | (DE-588)4621988-2 |
| title | A primer on the Dirichlet space |
| title_auth | A primer on the Dirichlet space |
| title_exact_search | A primer on the Dirichlet space |
| title_full | A primer on the Dirichlet space Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford |
| title_fullStr | A primer on the Dirichlet space Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford |
| title_full_unstemmed | A primer on the Dirichlet space Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford |
| title_short | A primer on the Dirichlet space |
| title_sort | a primer on the dirichlet space |
| topic | Dirichlet principle Hilbert space Holomorphic functions Functions of complex variables Dirichlet-Raum (DE-588)4621988-2 gnd |
| topic_facet | Dirichlet principle Hilbert space Holomorphic functions Functions of complex variables Dirichlet-Raum |
| url | https://doi.org/10.1017/CBO9781107239425 |
| work_keys_str_mv | AT elfallahomar aprimeronthedirichletspace |