Function theory of several complex variables:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Pacific Grove, Calif.
Wadsworth & Brooks/Cole
1992
|
| Edition: | 2. ed. |
| Series: | The Wadsworth & Brooks/Cole mathematics series
A Wiley interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 557 S. graph. Darst. |
| ISBN: | 0534170889 |
Staff View
MARC
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| 245 | 1 | 0 | |a Function theory of several complex variables |c Steven G. Krantz |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Pacific Grove, Calif. |b Wadsworth & Brooks/Cole |c 1992 | |
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| 650 | 4 | |a Fonctions de plusieurs variables complexes | |
| 650 | 7 | |a Fonctions de plusieurs variables complexes |2 ram | |
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Record in the Search Index
| _version_ | 1804122902296002560 |
|---|---|
| adam_text | Contents
0 An Introduction to the Subject 1
0.1 Preliminaries 1
0.2 What is a Holomorphic Function? 4
0.3 Comparison of C1 and Cn 5
1 Some Integral Formulas 17
1.1 The Bochner Martinelli Formula 17
1.2 Applications of Cauchy Theory and the d Equation 29
1.3 Basic Properties of Harmonic Functions 33
1.4 The Bergman Kernel 47
1.5 The Szego and Poisson Szego Kernels 63
1.6 Afterword to Chapter 1 67
EXERCISES 67
2 Subharmonicity and Its Applications 79
2.1 Subharmonic Functions 79
2.2 Pluriharmonic and Plurisubharmonic Functions 91
2.3 Power Series 96
xi
xii Contents
2.4 Hartogs s Theorem on Separate Analyticity 105
EXERCISES 108
3 Convexity 113
3.1 Many Notions of Convexity 113
3.2 Convexity and Pseudoconvexity 128
3.3 Pseudoconvexity, Plurisubharmonicity, and Analytic
Discs 138
3.4 Domains of Holomorphy 147
3.5 Examples of Domains of Holomorphy and the
Edge of the Wedge Theorem 155
EXERCISES 160
4 Hormander s Solution of the d Equation 171
4.1 Generalities about the B Problem 171
4.2 Unbounded Operators on a Hilbert Space 172
4.3 The Formalism of the d Problem 175
4.4 Some Computations 178
4.5 An Existence Theorem for the 8 Operator 186
4.6 A Regularity Theorem for the 5 Operator 190
EXERCISES 197
5 Solution of the Levi Problem and
Other Applications of 8 Techniques 209
5.1 An Extension Problem 209
5.2 Singular Functions on Strongly Pseudoconvex
Domains 212
5.3 Hefer s Lemma and Henkins Integral Representation 218
Contents xiii
5.4 Approximation Problems 224
EXERCISES 227
6 Cousin Problems, Cohomology,
and Sheaves 239
6.1 Cousin Problems 239
6.2 Sheaves 250
6.3 Dolbeault Isomorphism 264
6.4 Algebraic Properties of the Ring of Germs of Holomorphic
Functions 270
6.5 Sheaf of Divisors, Chern Classes, and the Obstruction to
Solving Cousin II 277
EXERCISES 281
7 The Zero Set of a Holomorphic Function 289
7.1 Coherent Analytic Sheaves 289
7.2 Applications of the Cartan and Oka Theorems: The
Structure of Ideals 291
7.3 Zeroes of One Holomorphic Function 294
7.4 Zero Sets for Different tfp Spaces are Different 298
7.5 Zero Sets of Hp Functions Do Not Have a Simple Mass
Distribution Characterization 303
EXERCISES 306
8 Some Harmonic Analysis 315
8.1 Review of the Classical Theory of Hv Spaces on the
Disc 315
8.2 Three Propositions about the Poisson Kernel 324
8.3 Subharmonicity, Harmonic Majorants, and Boundary
Values 331
xiv Contents
8.4 Pointwise Convergence for Harmonic Functions on Domains
in RN 338
8.5 Boundary Values of Holomorphic Functions in C 340
8.6 Admissible Convergence 345
8.7 The Lindelof Principle 356
8.8 Additional Tangential Phenomena: Lipschitz Spaces 359
EXERCISES 365
9 Constructive Methods 375
9.1 The Story of the Inner Functions Problem 375
9.2 Hakim/L0w/Sibony Construction of Inner Functions 379
9.3 Further Results Obtained with Constructive Methods 389
EXERCISES 395
10 Integral Formulas for Solutions to the 8
Problem and Norm Estimates 397
10.1 The Henkin Integral Formula 397
10.2 Estimates for the Henkin Solution on Domains in C2 401
10.3 Smoothness of the Henkin Solution and the Case of
Arbitrary d Closed Forms 405
10.4 First Cousin Problem with Bounds and Uniform
Approximation on Strongly Pseudoconvex Domains in
C2 412
EXERCISES 414
11 Holomorphic Mappings and Invariant
Metrics 423
11.1 The Classical Theory of Holomorphic Mappings 423
11.2 Invariant Metrics 429
Contents xv
11.3 The Theorem of Bun Wong and Rosay 437
11.4 Smoothness to the Boundary of Biholomorphic
Mappings 447
11.5 The Concept of Finite Type 456
11.6 Complex Analytic Dynamics 470
EXERCISES 474
APPENDIX I Manifolds 487
APPENDIX II Area Measures 489
APPENDIX III Exterior Algebra 491
APPENDIX IV Vectors, Covectors, and Differential
Forms 495
List of Notation 501
BIBLIOGRAPHY 507
INDEX 545
|
| any_adam_object | 1 |
| author | Krantz, Steven G. 1951- |
| author_GND | (DE-588)130535907 |
| author_facet | Krantz, Steven G. 1951- |
| author_role | aut |
| author_sort | Krantz, Steven G. 1951- |
| author_variant | s g k sg sgk |
| building | Verbundindex |
| bvnumber | BV008569782 |
| 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 780 |
| classification_tum | MAT 320f |
| ctrlnum | (OCoLC)25051271 (DE-599)BVBBV008569782 |
| dewey-full | 515/.94 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.94 |
| dewey-search | 515/.94 |
| dewey-sort | 3515 294 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV008569782 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:21:15Z |
| institution | BVB |
| isbn | 0534170889 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005632524 |
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| physical | XV, 557 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Wadsworth & Brooks/Cole |
| record_format | marc |
| series2 | The Wadsworth & Brooks/Cole mathematics series A Wiley interscience publication |
| spelling | Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut Function theory of several complex variables Steven G. Krantz 2. ed. Pacific Grove, Calif. Wadsworth & Brooks/Cole 1992 XV, 557 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Wadsworth & Brooks/Cole mathematics series A Wiley interscience publication Fonctions de plusieurs variables complexes Fonctions de plusieurs variables complexes ram Functions of several complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s DE-604 Mehrere komplexe Variable (DE-588)4169285-8 s 1\p DE-604 Funktion Mathematik (DE-588)4071510-3 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005632524&sequence=000002&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 |
| spellingShingle | Krantz, Steven G. 1951- Function theory of several complex variables Fonctions de plusieurs variables complexes Fonctions de plusieurs variables complexes ram Functions of several complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| subject_GND | (DE-588)4169285-8 (DE-588)4018935-1 (DE-588)4277015-4 (DE-588)4071510-3 |
| title | Function theory of several complex variables |
| title_auth | Function theory of several complex variables |
| title_exact_search | Function theory of several complex variables |
| title_full | Function theory of several complex variables Steven G. Krantz |
| title_fullStr | Function theory of several complex variables Steven G. Krantz |
| title_full_unstemmed | Function theory of several complex variables Steven G. Krantz |
| title_short | Function theory of several complex variables |
| title_sort | function theory of several complex variables |
| topic | Fonctions de plusieurs variables complexes Fonctions de plusieurs variables complexes ram Functions of several complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| topic_facet | Fonctions de plusieurs variables complexes Functions of several complex variables Mehrere komplexe Variable Funktionentheorie Mehrere Variable Funktion Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005632524&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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