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Bibliographic Details
Main Authors:	Duren, Peter L. 1935-2020 (Author), Schuster, Alexander 1968- (Author)
Format:	Book
Language:	English
Published:	Providence, Rhode Island American Mathematical Society [2004]
Series:	Mathematical surveys and monographs Volume 100
Subjects:	Bergman, Espaces de Espaços de banach Funções de uma variável complexa Ruimten (wiskunde) Bergman spaces Bergman-Raum
Links:	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
Physical Description:	x, 318 Seiten
ISBN:	0821808109 9780821808108

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Record in the Search Index

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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
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author	Duren, Peter L. 1935-2020 Schuster, Alexander 1968-
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indexdate	2024-12-20T11:58:46Z
institution	BVB
isbn	0821808109 9780821808108
language	English
lccn	2003063825
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physical	x, 318 Seiten
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publisher	American Mathematical Society
record_format	marc
series	Mathematical surveys and monographs
series2	Mathematical surveys and monographs
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
volume_link	(DE-604)BV000018014
work_keys_str_mv	AT durenpeterl bergmanspaces AT schusteralexander bergmanspaces

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