Holomorphic functions and integral representations in several complex variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; NY
Springer New York
[2010]
|
| Ausgabe: | Corrected second printing. Softcover version of original hardcover edition 1986 |
| Schriftenreihe: | Graduate Texts in Mathematics
108 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XViii, 386 Seiten Diagramme |
| ISBN: | 9781441930781 1441930787 |
Internformat
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| 245 | 1 | 0 | |a Holomorphic functions and integral representations in several complex variables |c R. Michael Range |
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| 300 | |a XViii, 386 Seiten |b Diagramme | ||
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Datensatz im Suchindex
| _version_ | 1806414474649796608 |
|---|---|
| adam_text |
Contents
Suggestions for the Reader
Interdependence of the Chapters
CHAPTER I
Elementary Local Properties of Holomorphic Functions
§1. Holomorphic Functions
§2. Holomorphic Maps
§3. Zero Sets of Holomorphic Functions
Notes for Chapter I
CHAPTER II
Domains of Holomorphy and Pseudoconvexity
§1. Elementary Extension Phenomena
§2. Natural Boundaries and Pseudoconvexity
§3, The Convexity Theory of Cartan and Thullen
§4. Plurisubharmonic Functions
§5. Characterizations of Pseudoconvexity
Notes for Chapter II
CHAPTER III
Differential Forms and Hermitian Geometry
§1. Calculus on Real Differentiable Manifolds
§2. Complex Structures
§3. Hermitian Geometry in C"
Notes for Chapter III
XIV
Contents
CHAPTER IV
Integral Representations in C” 144
§1. The Bochner-Martinelli-Koppelman Formula 145
§2. Some Applications 159
§3. The General Homotopy Formula 168
§4. The Bergman Kernel 179
Notes for Chapter IV 187
CHAPTER V
The Levi Problem and the Solution of 8 on Strictly Pseudoconvex
Domains 191
§1. A Parametrix for 3 on Strictly Pseudoconvex Domains 192
§2. A Solution Operator for d 197
§3. The Lipschitz 1/2-Estimate 204
Notes for Chapter V 212
CHAPTER VI
Function Theory on Domains of Holomorphy in Cn 214
§1. Approximation and Exhaustions 215
§2. d-Cohomological Characterization of Stein Domains 225
§3. Topological Properties of Stein Domains 227
§4. Meromorphic Functions and the Additive Cousin Problem 230
§5. Holomorphic Functions with Prescribed Zeroes 237
§6. Preview: Cohomology of Coherent Analytic Sheaves 250
Notes for Chapter VI 270
CHAPTER VII
Topics in Function Theory on Strictly Pseudoconvex Domains 273
§1. A Cauchy Kernel for Strictly Pseudoconvex Domains 274
§2. Uniform Approximation on D 280
§3. The Kernel of Henkin and Ramirez 283
§4. Gleason’s Problem and Decomposition in A(D) 290
§5. U Estimates for Solutions of d 294
§6. Approximation of Holomorphic Functions in Lp Norm 303
§7. Regularity Properties of the Bergman Projection 307
§8. Boundary Regularity of Biholomorphic Maps 324
§9. The Reflection Principle 340
Notes for Chapter VII 349
Contents
XV
Appendix A 356
Appendix B 358
Appendix C 360
Bibliography 363
Glossary of Symbols and Notations 374
Index 379 |
| any_adam_object | 1 |
| author | Range, R. Michael 1944- |
| author_GND | (DE-588)1081491507 |
| author_facet | Range, R. Michael 1944- |
| author_role | aut |
| author_sort | Range, R. Michael 1944- |
| author_variant | r m r rm rmr |
| building | Verbundindex |
| bvnumber | BV044854445 |
| classification_rvk | SK 750 |
| ctrlnum | (OCoLC)1028924949 (DE-599)DNB1008415626 |
| discipline | Mathematik |
| edition | Corrected second printing. Softcover version of original hardcover edition 1986 |
| format | Book |
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| id | DE-604.BV044854445 |
| illustrated | Not Illustrated |
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| isbn | 9781441930781 1441930787 |
| language | English |
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| physical | XViii, 386 Seiten Diagramme |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer New York |
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| series2 | Graduate Texts in Mathematics |
| spelling | Range, R. Michael 1944- (DE-588)1081491507 aut Holomorphic functions and integral representations in several complex variables R. Michael Range Corrected second printing. Softcover version of original hardcover edition 1986 New York ; NY Springer New York [2010] © 2010 XViii, 386 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate Texts in Mathematics 108 Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 s Holomorphe Funktion (DE-588)4025645-5 s Mehrere komplexe Variable (DE-588)4169285-8 s DE-604 Funktion Mathematik (DE-588)4071510-3 s Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 2\p DE-604 3\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4757-1918-5 Graduate Texts in Mathematics 108 (DE-604)BV000000067 108 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3598062&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030249255&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Range, R. Michael 1944- Holomorphic functions and integral representations in several complex variables Graduate Texts in Mathematics Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Funktionentheorie (DE-588)4018935-1 gnd Integraldarstellung (DE-588)4127585-8 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4169285-8 (DE-588)4071510-3 (DE-588)4025645-5 (DE-588)4018935-1 (DE-588)4127585-8 (DE-588)4277015-4 |
| title | Holomorphic functions and integral representations in several complex variables |
| title_auth | Holomorphic functions and integral representations in several complex variables |
| title_exact_search | Holomorphic functions and integral representations in several complex variables |
| title_full | Holomorphic functions and integral representations in several complex variables R. Michael Range |
| title_fullStr | Holomorphic functions and integral representations in several complex variables R. Michael Range |
| title_full_unstemmed | Holomorphic functions and integral representations in several complex variables R. Michael Range |
| title_short | Holomorphic functions and integral representations in several complex variables |
| title_sort | holomorphic functions and integral representations in several complex variables |
| topic | Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Funktionentheorie (DE-588)4018935-1 gnd Integraldarstellung (DE-588)4127585-8 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Mehrere komplexe Variable Funktion Mathematik Holomorphe Funktion Funktionentheorie Integraldarstellung Mehrere Variable |
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