Analytic functions of several complex variables:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS Chelsea Publ.
2009
|
| Edition: | Repr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke Originally published: Englewood Cliffs, N.J. : Prentice-Hall, 1965, in series: Prentice-Hall series in modern analysis. |
| Physical Description: | XII, 317 S. |
| ISBN: | 9780821821657 |
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MARC
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| 100 | 1 | |a Gunning, Robert C. |d 1931- |e Verfasser |0 (DE-588)119324326 |4 aut | |
| 245 | 1 | 0 | |a Analytic functions of several complex variables |c Robert C. Gunning, Hugo Rossi |
| 250 | |a Repr. | ||
| 264 | 1 | |a Providence, RI |b AMS Chelsea Publ. |c 2009 | |
| 300 | |a XII, 317 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Originally published: Englewood Cliffs, N.J. : Prentice-Hall, 1965, in series: Prentice-Hall series in modern analysis. | ||
| 650 | 4 | |a Functions of several complex variables | |
| 650 | 4 | |a Functional analysis | |
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Record in the Search Index
| _version_ | 1804141132094898176 |
|---|---|
| adam_text | CONTENTS
Chapter I
—
Holomorphic Functions
A The Elementary Properties of Holomorphic Functions
.... 1
В
Holomorphic Mappings and Complex Manifolds
...... 13
С
Removable Singularities
................. 19
D
The Calculus of Differential Forms
............ 22
E
The Cousin Theorem
........................ 31
F
Polynomial Approximations
................ 36
G
Envelopes of Holomorphy
................ 43
H
Some Applications to Uniform Algebras
.......... 55
Notes
......................... 63
Chapter II
—
Local Rings of Holomorphic Functions
65
A The Elementary Properties of the Local Rings
........ 65
В
The
Weierstrass
Theorems
................ 67
С
Modules Over the Local Rings
.............. 73
D
The Extended
Weierstrass
Division Theorem
........ 79
E
Germs of Varieties
.................... 85
Notes
......................... 92
Chapter III—Varieties
93
A The
Nullstellensatz
for Prime Ideals, and Local Parametrization
93
В
Analytic Covers
..................... 101
С
Dimension
....................... 110
Notes
......................... 117
Chapter IV—Analytic Sheaves
118
A The Elementary Properties of Sheaves
........... 118
В
Sheaves of Modules
................... 124
С
Analytic Sheaves on
Subdomains
of
<Ľn
........... 133
D
Analytic Sheaves on Subvarieties of C
........... 138
Notes
......................... 146
Chapter V—Analytic Spaces
147
A Definitions and Examples
................. 147
В
Holomorphic Functions on an Analytic Space
........ 155
С
The Proper Mapping Theorem
.............. 160
D
Nowhere Degenerate Maps
................ 166
Notes
......................... 171
Chapter VI—Cohomology Theory
172
A Soft Sheaves and Fine Sheaves
.............. 172
В
The Axioms of Sheaf Cohomology
............. 175
С
The Theorem of Dolbeault on Cohomology
......... 183
D
Leray s Theorem on Cohomology
............. 186
E
Cartan s Lemma
..................... 192
F
Amalgamation of Syzygies
............... . 201
Notes
......................... 207
Chapter
VII—
Stein Spaces, Geometric Theory
208
A Approximation Theorems
................. 208
В
Special Analytic Polyhedra
................ 215
С
The Imbedding Theorem
................. 219
D
Uses of Special Analytic Polyhedra
............. 226
Notes
......................... 233
Chapter
VIII—
Stein Spaces, Sheaf Theory
234
A Frechet Sheaves
..................... 234
В
Meromorphic Functions
................ . 246
С
Locally Free Sheaves
................... 252
Notes
......................... 259
Chapter IX
—
Pseudoconvexity
260
A The Complex Hessian
.................. 260
В
Grauert s Solution of Levi s Problem
........... . 264
С
Plurisubharmonic Functions
............... . 271
D
Oka s Pseudoconvexity Theorem
............. 279
E Kodaira s
Theorem on
Projective
Varieties
......... 284
Notes
......................... 287
Appendix A—Partitions of Unity
288
Appendix B—
The Theorem of Schwartz on Frechet Spaces
290
References and Bibliography
296
Index
313
|
| any_adam_object | 1 |
| author | Gunning, Robert C. 1931- Rossi, Hugo 1935- |
| author_GND | (DE-588)119324326 (DE-588)174028520 |
| author_facet | Gunning, Robert C. 1931- Rossi, Hugo 1935- |
| author_role | aut aut |
| author_sort | Gunning, Robert C. 1931- |
| author_variant | r c g rc rcg h r hr |
| building | Verbundindex |
| bvnumber | BV036077146 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 780 |
| ctrlnum | (OCoLC)417444198 (DE-599)BVBBV036077146 |
| 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 | Repr. |
| format | Book |
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| id | DE-604.BV036077146 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:11:00Z |
| institution | BVB |
| isbn | 9780821821657 |
| language | English |
| lccn | 2009025418 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018968288 |
| oclc_num | 417444198 |
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| owner_facet | DE-739 DE-11 DE-703 |
| physical | XII, 317 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | AMS Chelsea Publ. |
| record_format | marc |
| spelling | Gunning, Robert C. 1931- Verfasser (DE-588)119324326 aut Analytic functions of several complex variables Robert C. Gunning, Hugo Rossi Repr. Providence, RI AMS Chelsea Publ. 2009 XII, 317 S. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Originally published: Englewood Cliffs, N.J. : Prentice-Hall, 1965, in series: Prentice-Hall series in modern analysis. Functions of several complex variables Functional analysis Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 Komplexe Variable (DE-588)4164905-9 s 2\p DE-604 Analytische Funktion (DE-588)4142348-3 s 3\p DE-604 Rossi, Hugo 1935- Verfasser (DE-588)174028520 aut Erscheint auch als Online-Ausgabe 978-1-4704-1576-1 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018968288&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gunning, Robert C. 1931- Rossi, Hugo 1935- Analytic functions of several complex variables Functions of several complex variables Functional analysis Mehrere Variable (DE-588)4277015-4 gnd Komplexe Variable (DE-588)4164905-9 gnd Analytische Funktion (DE-588)4142348-3 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4277015-4 (DE-588)4164905-9 (DE-588)4142348-3 (DE-588)4018935-1 |
| title | Analytic functions of several complex variables |
| title_auth | Analytic functions of several complex variables |
| title_exact_search | Analytic functions of several complex variables |
| title_full | Analytic functions of several complex variables Robert C. Gunning, Hugo Rossi |
| title_fullStr | Analytic functions of several complex variables Robert C. Gunning, Hugo Rossi |
| title_full_unstemmed | Analytic functions of several complex variables Robert C. Gunning, Hugo Rossi |
| title_short | Analytic functions of several complex variables |
| title_sort | analytic functions of several complex variables |
| topic | Functions of several complex variables Functional analysis Mehrere Variable (DE-588)4277015-4 gnd Komplexe Variable (DE-588)4164905-9 gnd Analytische Funktion (DE-588)4142348-3 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Functions of several complex variables Functional analysis Mehrere Variable Komplexe Variable Analytische Funktion Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018968288&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gunningrobertc analyticfunctionsofseveralcomplexvariables AT rossihugo analyticfunctionsofseveralcomplexvariables |