Bergman spaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2004]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 100 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | x, 318 Seiten |
| ISBN: | 0821808109 9780821808108 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804132786697666560 |
|---|---|
| adam_text | MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 100 BERGMAN SPACES PETER
DUREN ALEXANDER SCHUSTER AMERICAN MATHEMATICAL SOCIETY V, *../*
CONTENTS PREFACE IX CHAPTER 0. OVERVIEW 1 CHAPTER 1. THE BERGMAN KERNEL
FUNCTION 7 1.1. POINT-EVALUATION FUNCTIONALS 7 1.2. ORTHONORMAL BASES 9
1.3. CONFORMAL INVARIANCE 12 1.4. AN EXTREMAL PROBLEM 14 1.5. CONNECTION
WITH GREEN S FUNCTION 16 1.6. THE BIHARMONIC GREEN FUNCTION 18 CHAPTER
2. LINEAR SPACE PROPERTIES 25 2.1. HARDY SPACES 25 2.2. STRICT AND
UNIFORM CONVEXITY 28 2.3. THE BERGMAN PROJECTION 30 2.4. DUAL SPACES 35
2.5. THE PSEUDOHYPERBOLIC METRIC 38 2.6. THE BLOCH SPACE 43 2.7.
HARMONIC CONJUGATES 54 2.8. LINEAR ISOMETRIES 56 2.9. FUNCTION
MULTIPLIERS 59 2.10. CARLESON MEASURES 61 2.11. UNIFORMLY DISCRETE
SEQUENCES 67 CHAPTER 3. ANALYTIC PROPERTIES * 73 3.1. MORE ON HARDY
SPACES 73 3.2. GROWTH OF FUNCTIONS IN BERGMAN SPACES . 77 3.3.
COEFFICIENTS OF FUNCTIONS IN BERGMAN SPACES 81 3.4. COEFFICIENT
MULTIPLIERS 86 3.5. KORENBLUM S MAXIMUM PRINCIPLE 90 VI CONTENTS CHAPTER
4. ZERO-SETS 93 4.1. PRELIMINARY REMARKS 93 4.2. DENSITY OF ZERO-SETS 96
4.3. DEPENDENCE ON P 98 4.4. UNIONS AND SUBSETS OF ZERO-SETS 101 4.5.
BLASCHKE PRODUCTS AS GENERATORS 106 4.6. UNIVERSAL DIVISORS 107 4.7.
PERTURBATIONS OF ZERO-SETS 114 4.8. ZEROS ON A RADIAL LINE 116 CHAPTER
5. CONTRACTIVE ZERO-DIVISORS 119 5.1. AN EXTREMAL PROBLEM 119 5.2.
EXPANSIVE MULTIPLIERS 127 5.3. PROOF OF THE INTEGRAL FORMULA 131 5.4.
REPRESENTATION BY KERNEL FUNCTIONS 137 5.5. ANALYTIC CONTINUATION 141
5.6. CONTRACTIVE DIVISORS 144 5.7. INVARIANT SUBSPACES 146 CHAPTER 6.
SAMPLING AND INTERPOLATION 153 6.1. DEFINITIONS AND MOTIVATIONS 153 6.2.
INTERPOLATION IN HARDY SPACES 157 6.3. A FAMILY OF SAMPLING AND
INTERPOLATION SEQUENCES 159 6.4. SOME EXPLICIT EXAMPLES 168 6.5. THE
DENSITY THEOREMS * 171 6.6. DIRECT CALCULATION OF DENSITIES 176 6.7.
SHARPENED FORMS OF HOROWITZ THEOREMS 182 6.8. SUFFICIENT CONDITIONS
WITH THE PSEUDOHYPERBOLIC METRIC 187 6.9. DUALITY RELATIONS 192 CHAPTER
7. PROOFS OF SAMPLING AND INTERPOLATION THEOREMS 197 7.1. PERTURBATION
OF SAMPLING SEQUENCES 197 7.2. NECESSITY OF THE SAMPLING CONDITION 204
7.3. SAMPLING IN THE GROWTH SPACE 207 7.4. SUFFICIENCY OF THE SAMPLING
CONDITION IN A P 216 7.5. SUFFICIENCY OF THE INTERPOLATION CONDITION 219
7.6. NECESSITY OF THE INTERPOLATION CONDITION 234 7.7. WEAK
INTERPOLATION 240 CHAPTER 8. INVARIANT SUBSPACES 245 8.1. BEURLING S
THEORY FOR HARDY SPACES 245 8.2. CYCLIC INNER FUNCTIONS IN BERGMAN
SPACES 247 8.3. CYCLIC ELEMENTS OF BERGMAN SPACES 258 8.4. THE INDEX OF
AN INVARIANT SUBSPACE 261 8.5. INVARIANT SUBSPACES OF HIGHER INDEX 263
8.6. GENERALIZATIONS TO AP 265 CONTENTS VII CHAPTER 9. STRUCTURE OF
INVARIANT SUBSPACES 271 9.1. DESCRIPTION OF GENERATORS 271 9.2. INNER
ANDOUTER FUNCTIONS FOR BERGMAN SPACES 273 9.3. GENERALIZATION OF THE
MAIN THEOREM 276 9.4. CYCLIC SUBSPACES OF A P 282 9.5. EXTREMAL
FUNCTIONS AS GENERATORS 288 REFERENCES 297 INDEX 313
|
| any_adam_object | 1 |
| author | Duren, Peter L. 1935-2020 Schuster, Alexander 1968- |
| author_GND | (DE-588)135675502 (DE-588)135676568 |
| author_facet | Duren, Peter L. 1935-2020 Schuster, Alexander 1968- |
| author_role | aut aut |
| author_sort | Duren, Peter L. 1935-2020 |
| author_variant | p l d pl pld a s as |
| building | Verbundindex |
| bvnumber | BV019354911 |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331.7 |
| callnumber-search | QA331.7 |
| callnumber-sort | QA 3331.7 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 SK 620 SK 700 |
| ctrlnum | (OCoLC)53477730 (DE-599)BVBBV019354911 |
| dewey-full | 519.9 515/.9 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics 515 - Analysis |
| dewey-raw | 519.9 515/.9 515.9 |
| dewey-search | 519.9 515/.9 515.9 |
| dewey-sort | 3519.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019354911 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:58:22Z |
| institution | BVB |
| isbn | 0821808109 9780821808108 |
| language | English |
| lccn | 2003063825 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012818861 |
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| physical | x, 318 Seiten |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Duren, Peter L. 1935-2020 Verfasser (DE-588)135675502 aut Bergman spaces Peter Duren ; Alexander Schuster Providence, Rhode Island American Mathematical Society [2004] © 2004 x, 318 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 100 Bergman, Espaces de Espaços de banach larpcal Funções de uma variável complexa larpcal Ruimten (wiskunde) gtt Bergman spaces Bergman-Raum (DE-588)4347980-7 gnd rswk-swf Bergman-Raum (DE-588)4347980-7 s b DE-604 Schuster, Alexander 1968- Verfasser (DE-588)135676568 aut Erscheint auch als Online-Ausgabe 978-1-4704-1327-9 Mathematical surveys and monographs Volume 100 (DE-604)BV000018014 100 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012818861&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duren, Peter L. 1935-2020 Schuster, Alexander 1968- Bergman spaces Mathematical surveys and monographs Bergman, Espaces de Espaços de banach larpcal Funções de uma variável complexa larpcal Ruimten (wiskunde) gtt Bergman spaces Bergman-Raum (DE-588)4347980-7 gnd |
| subject_GND | (DE-588)4347980-7 |
| title | Bergman spaces |
| title_auth | Bergman spaces |
| title_exact_search | Bergman spaces |
| title_full | Bergman spaces Peter Duren ; Alexander Schuster |
| title_fullStr | Bergman spaces Peter Duren ; Alexander Schuster |
| title_full_unstemmed | Bergman spaces Peter Duren ; Alexander Schuster |
| title_short | Bergman spaces |
| title_sort | bergman spaces |
| topic | Bergman, Espaces de Espaços de banach larpcal Funções de uma variável complexa larpcal Ruimten (wiskunde) gtt Bergman spaces Bergman-Raum (DE-588)4347980-7 gnd |
| topic_facet | Bergman, Espaces de Espaços de banach Funções de uma variável complexa Ruimten (wiskunde) Bergman spaces Bergman-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012818861&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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