Function theory of several complex variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
AMS Chelsea Publ.
2001
|
| Ausgabe: | 2. ed., printed with corr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 564 S. graph. Darst. |
| ISBN: | 0821827243 |
Internformat
MARC
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| 245 | 1 | 0 | |a Function theory of several complex variables |c by Steven G. Krantz |
| 250 | |a 2. ed., printed with corr. | ||
| 264 | 1 | |a Providence, RI |b AMS Chelsea Publ. |c 2001 | |
| 300 | |a XVI, 564 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a analyse complexe |2 inriac | |
| 650 | 7 | |a analyse harmonique |2 inriac | |
| 650 | 7 | |a fonction à plusieurs variables |2 inriac | |
| 650 | 7 | |a pseudo-convexité |2 inriac | |
| 650 | 7 | |a variable complexe |2 inriac | |
| 650 | 0 | 7 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |D s |
| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804128696325373952 |
|---|---|
| adam_text | Titel: Function theory of several complex variables
Autor: Krantz, Steven G.
Jahr: 2001
Contents
Preface to the Second Edition xiii
Preface to the First Edition xv
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 19
1.1 The Bochner-Martinelli Formula 19
1.2 Applications of Cauchy Theory and the B
Equation 31
1.3 Basic Properties of Harmonic Functions 35
1.4 The Bergman Kernel 49
1.5 The Szegö and Poisson-Szegö Kernels 66
viii Contents
1.6 Afterword to Chapter 1 69
EXERCISES 70
2 Subharmonicity and
Its Applications 81
2.1 Subharmonic Functions 81
2.2 Pluriharmonic and Plurisubharmonic Functions 94
2.3 Power Series 99
2.4 Hartogs s Theorem on Separate Analyticity 107
EXERCISES 110
3 Convexity 117
3.1 Many Notions of Convexity 117
3.2 Convexity and Pseudoconvexity 132
3.3 Pseudoconvexity, Plurisubharmonicity, and Analytic
Discs 142
3.4 Domains of Holomorphy 151
3.5 Examples of Domains of Holomorphy and the
Edge-of-the-Wedge Theorem 159
EXERCISES 164
4 Hörmander s Solution of the
d Equation 175
4.1 Generalities about the B Problem 175
Contents ix
4.2 Unbounded Operators on a Hubert Space 176
4.3 The Formalism of the 8 Problem 179
4.4 Some Computations 182
4.5 An Existence Theorem for the B Operator 190
4.6 A Regularity Theorem for the 9 Operator 194
EXERCISES 201
5 Solution of the Levi Problem
and Other Applications of
8 Techniques 213
5.1 An Extension Problem 213
5.2 Singular Functions on Strongly Pseudoconvex
Domains 216
5.3 Hefer s Lemma and Henkin s Integral
Representation 223
5.4 Approximation Problems 228
EXERCISES 231
6 Cousin Problems,
Cohomology, and Sheaves 243
6.1 Cousin Problems 243
6.2 Sheaves 254
6.3 Dolbeault Isomorphism 268
x Contents
6.4 Algebraic Properties of the Ring of Germs of
Holomorphic Functions 275
6.5 Sheaf of Divisors, Chern Classes, and the
Obstruction to Solving Cousin II 281
EXERCISES 286
7 The Zero Set of a
Holomorphic Function 293
7.1 Coherent Analytic Sheaves 293
7.2 Applications of the Cartan and Oka Theorems: The
Structure of Ideals 295
7.3 Zeros of One Holomorphic Function 298
7.4 Zero Sets for Different Hp Spaces Are Different 302
7.5 Zero Sets of Hp Functions Do Not Have a Simple
Mass Distribution Characterization 307
EXERCISES 310
8 Some Harmonic Analysis 321
8.1 Review of the Classical Theory of Hp Spaces on the
Disc 321
8.2 Three Propositions about the Poisson Kernel 330
8.3 Subharmonicity, Harmonic Majorants, and
Boundary Values 338
8.4 Pointwise Convergence for Harmonic Functions on
Domains in RN 344
Contents xi
8.5 Boundary Values of Holomorphic Functions in
C 346
8.6 Admissible Convergence 352
8.7 The Lindelöf Principle 362
8.8 Additional Tangential Phenomena: Lipschitz
Spaces 365
EXERCISES 371
9 Constructive Methods 381
9.1 Story of the Inner Functions Problem 381
9.2 The Hakim/L0w/Sibony Construction of Inner
Functions 385
9.3 Further Results Obtained with Constructive
Methods 395
EXERCISES 401
10 Integral Formulas for
Solutions to the B Problem
and Norm Estimates 403
10.1 The Henkin Integral Formula 403
10.2 Estimates for the Henkin Solution on Domains in
C2 407
10.3 Smoothness of the Henkin Solution and the Case of
Arbitrary 9-Closed Forms 411
xii Contents
10.4 First Cousin Problem with Bounds and Uniform
Approximation on Strongly Pseudoconvex Domains
in C2 418
EXERCISES 421
11 Holomorphic Mappings and
Invariant Metrics 429
11.1 Classical Theory of Holomorphic Mappings 429
11.2 Invariant Metrics 434
11.3 The Theorem of Bun Wong and Rosay 443
11.4 Smoothness to the Boundary of Biholomorphic
Mappings 453
11.5 Concept of Finite Type 462
11.6 Complex Analytic Dynamics 476
EXERCISES 480
Appendix I Manifolds 493
Appendix II Area Measures 495
Appendix III Exterior Algebra 499
Appendix IV Vectors, Covectors, and Differential
Forms 503
List of Notation 509
Bibliography 515
Index 553
|
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| author | Krantz, Steven G. 1951- |
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| building | Verbundindex |
| bvnumber | BV013862175 |
| classification_rvk | SK 780 |
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| discipline | Mathematik |
| edition | 2. ed., printed with corr. |
| format | Book |
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| id | DE-604.BV013862175 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:53:21Z |
| institution | BVB |
| isbn | 0821827243 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009481430 |
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| physical | XVI, 564 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | AMS Chelsea Publ. |
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| spelling | Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut Function theory of several complex variables by Steven G. Krantz 2. ed., printed with corr. Providence, RI AMS Chelsea Publ. 2001 XVI, 564 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier analyse complexe inriac analyse harmonique inriac fonction à plusieurs variables inriac pseudo-convexité inriac variable complexe inriac 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 komplexe Variable (DE-588)4169285-8 s DE-604 Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 Funktion Mathematik (DE-588)4071510-3 s 2\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2991-1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009481430&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 analyse complexe inriac analyse harmonique inriac fonction à plusieurs variables inriac pseudo-convexité inriac variable complexe inriac 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 by Steven G. Krantz |
| title_fullStr | Function theory of several complex variables by Steven G. Krantz |
| title_full_unstemmed | Function theory of several complex variables by Steven G. Krantz |
| title_short | Function theory of several complex variables |
| title_sort | function theory of several complex variables |
| topic | analyse complexe inriac analyse harmonique inriac fonction à plusieurs variables inriac pseudo-convexité inriac variable complexe inriac 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 | analyse complexe analyse harmonique fonction à plusieurs variables pseudo-convexité variable complexe 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=009481430&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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