Function theory of several complex variables:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS Chelsea Publ.
2008
|
| Edition: | 2. ed., printed with corr., [Nachdr.] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Nebentitel: Several complex variables |
| Physical Description: | XVI, 564 S. graph. Darst. |
| ISBN: | 9780821827246 0821827243 |
Staff View
MARC
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| 100 | 1 | |a Krantz, Steven G. |d 1951- |e Verfasser |0 (DE-588)130535907 |4 aut | |
| 245 | 1 | 0 | |a Function theory of several complex variables |c by Steven G. Krantz |
| 250 | |a 2. ed., printed with corr., [Nachdr.] | ||
| 264 | 1 | |a Providence, RI |b AMS Chelsea Publ. |c 2008 | |
| 300 | |a XVI, 564 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Nebentitel: Several complex variables | ||
| 650 | 0 | 7 | |a Mehrere Variable |0 (DE-588)4277015-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804143497867952128 |
|---|---|
| adam_text | 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
В
Equation
31
1.3
Basic Properties of Harmonic Functions
35
1.4
The Bergman Kernel
49
1.5
The
Szegő
and
Poisson-Szegö
Kernels
66
vii
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
3
Equation
175
4.1
Generalities about the
В
Problem
175
Contents ix
4.2
Unbounded
Operators
on a Hubert Space
176
4.3
The Formalism of the
В
Problem
179
4.4
Some Computations
182
4.5
An Existence Theorem for the
3
Operator
190
4.6
A Regularity Theorem for the
д
Operator
194
EXERCISES
201
5
Solution of the
Levi
Problem
and Other Applications of
д
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
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
№
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 Hv 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 MN
344
Contents xi
8.5
Boundary Values of Holomorphic Functions in
Cn
346
8.6
Admissible Convergence
352
8.7
The
Lindelof
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
8
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
ő-Closed
Forms
411
xii Contents
10.4 First Cousin Problem
with Bounds and
Uniform
Approximation
on Strongly Pseudoconvex
Domains
in
С2
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- |
| author_GND | (DE-588)130535907 |
| author_facet | Krantz, Steven G. 1951- |
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| author_sort | Krantz, Steven G. 1951- |
| author_variant | s g k sg sgk |
| building | Verbundindex |
| bvnumber | BV036804520 |
| classification_rvk | SK 780 |
| ctrlnum | (OCoLC)706015959 (DE-599)BVBBV036804520 |
| discipline | Mathematik |
| edition | 2. ed., printed with corr., [Nachdr.] |
| format | Book |
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| id | DE-604.BV036804520 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:48:36Z |
| institution | BVB |
| isbn | 9780821827246 0821827243 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020720627 |
| oclc_num | 706015959 |
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| owner_facet | DE-355 DE-BY-UBR DE-523 DE-83 DE-739 |
| physical | XVI, 564 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | AMS Chelsea Publ. |
| record_format | marc |
| 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., [Nachdr.] Providence, RI AMS Chelsea Publ. 2008 XVI, 564 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nebentitel: Several complex variables Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020720627&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 Mehrere Variable (DE-588)4277015-4 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4277015-4 (DE-588)4169285-8 (DE-588)4071510-3 (DE-588)4018935-1 |
| 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 | Mehrere Variable (DE-588)4277015-4 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Mehrere Variable Mehrere komplexe Variable Funktion Mathematik Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020720627&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT krantzsteveng functiontheoryofseveralcomplexvariables |