Pick interpolation and Hilbert function spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
2002
|
| Series: | Graduate studies in mathematics
44 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 308 S. |
| ISBN: | 9780821828984 0821828983 |
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MARC
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| 490 | 1 | |a Graduate studies in mathematics |v 44 | |
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Record in the Search Index
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| adam_text | PICK INTERPOLATION AND HILBERT FUNCTION SPACES JIM AGLER JOHN E.
MCCARTHY GRADUATE STUDIES IN MATHEMATICS VOLUME 44 ! F AMERICAN
MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND CONTENTS PREFACE XV
CHAPTER 0. PREREQUISITES AND NOTATION 1 §0.1. GENERAL NOTATION 1 §0.2.
BLASCHKE PRODUCTS 2 §0.3. PSEUDO-HYPERBOLIC METRIC 3 §0.4. HILBERT
SPACES 3 §0.5. THE WEAK-STAR TOPOLOGY ON B(H) 4 §0.6. RANK ONE OPERATORS
4 §0.7. ANALYTIC FUNCTIONS OF SEVERAL VARIABLES 5 CHAPTER 1.
INTRODUCTION 7 §1.1. THE PICK PROBLEM 7 §1.2. H AS AN OPERATOR ALGEBRA
9 §1.3. THE OPERATOR THEORY APPROACH TO THE PICK PROBLEM 10 §1.4. THE
PICK PROPERTY 10 §1.5. MODEL THEORY 11 §1.6. COLLECTIONS OF KERNELS 12
CHAPTER 2. KERNELS AND FUNCTION SPACES 15 §2.1. HILBERT FUNCTION SPACES
15 §2.2. KERNELS 17 §2.3. MULTIPLIERS 21 §2.4. TENSOR PRODUCTS 22 IX X
CONTENTS §2.5. VECTOR-VALUED HILBERT FUNCTION SPACES 23 §2.6. RESCALING
KERNELS 25 §2.7. FACTORING KERNELS 28 §2.8. OPERATOR-VALUED KERNELS 30
§2.9. HISTORICAL NOTES 33 CHAPTER 3. HARDY SPACES 35 §3.1. HP SPACES 35
§3.2. FATOU S THEOREM 36 §3.3. H P SPACES AGAIN 41 §3.4. #(ID ) AS A
MULTIPLIER ALGEBRA 43 §3.5. INNER FUNCTIONS 45 §3.6. HISTORICAL NOTES 48
CHAPTER 4. P 2 (/_I) 49 §4.1. OTHER SPACES WITH H(TD ) AS THE
MULTIPLIER ALGEBRA 49 §4.2. VECTOR-VALUED -P 2 (/U) SPACES 52 CHAPTER 5.
PICK REDUX 55 §5.1. NECESSITY OF POSITIVITY OF THE PICK MATRIX 55 §5.2.
THE SZEGO KERNEL HAS THE PICK PROPERTY 59 §5.3. THE CARATHEODORY PROBLEM
65 §5.4. UNIQUENESS OF THE SZEGO KERNEL 67 §5.5. HISTORICAL NOTES 69
CHAPTER 6. QUALITATIVE PROPERTIES OF THE SOLUTION OF THE PICK PROBLEM IN
H(B) 71 §6.1. A FORMULA FOR THE SOLUTION 71 §6.2. THE REALIZATION
FORMULA FOR H(B) 73 §6.3. ANOTHER FORMULA FOR THE SOLUTION 76 §6.4.
THE NEVANLINNA PROBLEM 78 CHAPTER 7. CHARACTERIZING KERNELS WITH THE
COMPLETE PICK PROPERTY 79 §7.1. CHARACTERIZATION OF THE COMPLETE PICK
PROPERTY 79 §7.2. ANOTHER CHARACTERIZATION OF THE COMPLETE PICK PROPERTY
87 §7.3. HOLOMORPHIC SPACES WITH THE COMPLETE PICK PROPERTY 88 §7.4. THE
SOBOLEV SPACE 91 §7.5. THE M SXT PICK PROPERTY 94 §7.6. HISTORICAL NOTES
95 CONTENTS XI CHAPTER 8. THE UNIVERSAL PICK KERNEL 97 §8.1. THE
UNIVERSAL KERNEL 97 §8.2. THE REALIZATION FORMULA FOR THE UNIVERSAL
KERNEL 101 §8.3. QUALITATIVE PROPERTIES OF SOLUTIONS OF THE PICK PROBLEM
FOR COMPLETE PICK KERNELS 105 §8.4. THE TOEPLITZ-CORONA THEOREM 111
§8.5. BEURLING THEOREMS 114 §8.6. HOLOMORPHIC COMPLETE PICK SPACES 117
§8.7. THE NEVANLINNA PROBLEM 118 §8.8. UNIQUENESS OF KERNELS WITH THE
PICK PROPERTY 123 §8.9. HISTORICAL NOTES 124 CHAPTER 9. INTERPOLATING
SEQUENCES 125 §9.1. INTERPOLATING SEQUENCES FOR H(B) 125 §9.2.
GRAMMIANS, CARLESON MEASURES AND RIESZ SYSTEMS 126 §9.3. INTERPOLATING
SEQUENCES AND THE PICK PROPERTY 133 §9.4. ZERO SETS 135 §9.5. GRAMMIANS
BOUNDED ABOVE AND BELOW 140 §9.6. CARLESON S INTERPOLATION THEOREM 145
§9.7. HISTORICAL NOTES 148 CHAPTER 10. MODEL THEORY I: ISOMETRIES 151
§10.1. DILATIONS AND EXTENSIONS 151 §10.2. THE SZ.-NAGY DILATION THEOREM
153 §10.3. THE STRUCTURE OF ISOMETRIES 156 §10.4. VON NEUMANN S
INEQUALITY 158 §10.5. ANDO S THEOREM 160 §10.6. THE COMMUTANT LIFTING
THEOREM 162 §10.7. THREE OR MORE CONTRACTIONS 163 §10.8. HISTORICAL
NOTES 165 CHAPTER 11. THE BIDISK 167 §11.1. THE REALIZATION FORMULA -
SCALAR CASE 168 §11.2. THE REALIZATION FORMULA - MATRIX CASE 173 §11.3.
THE PICK THEOREM FOR THE BIDISK 180 §11.4. TOEPLITZ-CORONA FOR THE
BIDISK 182 §11.5. THE NEVANLINNA PROBLEM FOR THE BIDISK 185 XII CONTENTS
§11.6. A TWO POINT EXAMPLE 187 §11.7. INTERPOLATING SEQUENCES 190 §11.8.
THE POLYDISK 192 §11.9. OPEN PROBLEMS 192 §11.10. EXERCISES 193 §11.11.
HISTORICAL NOTES 193 CHAPTER 12. THE EXTREMAL THREE POINT PROBLEM ON D 2
195 §12.1. THE TWO POINT PROBLEM 195 §12.2. THE NON-DEGENERATE EXTREMAL
THREE POINT PROBLEM: THE STRICTLY 2-DIMENSIONAL CASE 197 §12.3. FINDING
F AND A IN THE STRICTLY 2-DIMENSIONAL CASE 204 §12.4. THE NON-DEGENERATE
EXTREMAL THREE POINT PROBLEM: THE NOT STRICTLY 2-DIMENSIONAL CASE 206
§12.5. PROBLEMS 209 §12.6. HISTORICAL NOTES 209 CHAPTER 13. COLLECTIONS
OF KERNELS 211 §13.1. AN ABSTRACT THEORY 211 §13.2. UNIFORM ALGEBRAS:
THE COLE-LEWIS-WERMER APPROACH 214 §13.3. FINITELY CONNECTED DOMAINS 219
§13.4. WHEN DOES A COLLECTION OF KERNELS HAVE THE PICK PROPERTY? 222
§13.5. HISTORICAL NOTES 235 CHAPTER 14. MODEL THEORY II: FUNCTION SPACES
237 §14.1. THEOREMS OF STINESPRING AND ARVESON 237 §14.2. HEREDITARY
FUNCTIONAL CALCULUS 243 §14.3. CO-ANALYTIC EXTENSIONS 247 §14.4. THE
TAYLOR SPECTRUM 252 §14.5. CO-ANALYTIC MODELS FOR M-TUPLES 255 §14.6.
VON NEUMANN INEQUALITIES 260 §14.7. HISTORICAL NOTES 260 CHAPTER 15.
LOCALIZATION 263 §15.1. LOCALIZATION OF EXTENSIONS 263 §15.2. KERNELS
WITH THE M SXS PICK PROPERTY 266 §15.3. LOCALIZATION OF DILATIONS 270
§15.4. HISTORICAL NOTES 272 CONTENTS XIII APPENDIX A. SCHUR PRODUCTS 273
APPENDIX B. PARROTT S LEMMA 277 APPENDIX C. RIESZ INTERPOLATION 281
APPENDIX D. THE SPECTRAL THEOREM FOR NORMAL M-TUPLES 287 §D.L. NORMAL
TUPLES 287 §D.2. COMMUTING ISOMETRIES 290 BIBLIOGRAPHY 293 INDEX 303
|
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| isbn | 9780821828984 0821828983 |
| language | English |
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| series2 | Graduate studies in mathematics |
| spelling | Agler, Jim 1951- Verfasser (DE-588)1185705627 aut Pick interpolation and Hilbert function spaces Jim Agler ; John E. McCarthy Providence, RI AMS 2002 XIX, 308 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 44 ESPAÇOS DE HILBERT larpcal Fonctions d'une variable complexe Hilbert, Espace de Interpolation Functions of complex variables Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s Interpolation (DE-588)4162121-9 s Komplexe Variable (DE-588)4164905-9 s DE-604 McCarthy, John E. 1964- Verfasser (DE-588)1056135700 aut Erscheint auch als Online-Ausgabe 978-1-4704-2095-6 Graduate studies in mathematics 44 (DE-604)BV009739289 44 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009722836&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Agler, Jim 1951- McCarthy, John E. 1964- Pick interpolation and Hilbert function spaces Graduate studies in mathematics ESPAÇOS DE HILBERT larpcal Fonctions d'une variable complexe Hilbert, Espace de Interpolation Functions of complex variables Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd Interpolation (DE-588)4162121-9 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4162121-9 (DE-588)4164905-9 |
| title | Pick interpolation and Hilbert function spaces |
| title_auth | Pick interpolation and Hilbert function spaces |
| title_exact_search | Pick interpolation and Hilbert function spaces |
| title_full | Pick interpolation and Hilbert function spaces Jim Agler ; John E. McCarthy |
| title_fullStr | Pick interpolation and Hilbert function spaces Jim Agler ; John E. McCarthy |
| title_full_unstemmed | Pick interpolation and Hilbert function spaces Jim Agler ; John E. McCarthy |
| title_short | Pick interpolation and Hilbert function spaces |
| title_sort | pick interpolation and hilbert function spaces |
| topic | ESPAÇOS DE HILBERT larpcal Fonctions d'une variable complexe Hilbert, Espace de Interpolation Functions of complex variables Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd Interpolation (DE-588)4162121-9 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| topic_facet | ESPAÇOS DE HILBERT Fonctions d'une variable complexe Hilbert, Espace de Interpolation Functions of complex variables Hilbert space Hilbert-Raum Komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009722836&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT aglerjim pickinterpolationandhilbertfunctionspaces AT mccarthyjohne pickinterpolationandhilbertfunctionspaces |