Function theory in several complex variables:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2001
|
| Series: | Translations of mathematical monographs
193 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Japan. übers. |
| Physical Description: | XIII, 366 S. graph. Darst. |
| ISBN: | 0821808168 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface ix
Preface to the English Edition xiii
Part 1. Fundamental Theory 1
Chapter 1. Holomorphic Functions and Domains of Holomorphy 3
1.1. Complex Euclidean Space 3
1.2. Analytic Functions 8
1.3. Holomorphic Functions 12
1.4. Separate Analyticity Theorem 23
1.5. Domains of Holomorphy 27
Chapter 2. Implicit Functions and Analytic Sets 37
2.1. Implicit Functions 37
2.2. Analytic Sets (Local) 44
2.3. Weierstrass Condition 56
2.4. Analytic Sets (Global) 60
2.5. Projections of Analytic Sets in Projective Space 64
Chapter 3. The Poincare, Cousin, and Runge Problems 73
3.1. Meromorphic Functions 73
3.2. Cousin Problems in Polydisks 77
3.3. Cousin I Problem in Polynomially Convex Domains 80
3.4. Cousin I Problem in Domains of Holomorphy 85
3.5. Cousin II Problem 91
3.6. Runge Problem 98
Chapter 4. Pseudoconvex Domains and Pseudoconcave Sets 105
4.1. Pseudoconvex Domains 105
4.2. Pseudoconvex Domains with Smooth Boundary 116
4.3. Boundary Problem 124
4.4. Pseudoconcave Sets 131
4.5. Analytic Derived Sets 137
Chapter 5. Holomorphic Mappings 147
5.1. Holomorphic Mappings of Elementary Domains 147
5.2. Holomorphic Mappings of C 152
vii
viii CONTENTS
Part 2. Theory of Analytic Spaces 165
Chapter 6. Ramified Domains 167
6.1. Ramified Domains 167
6.2. Fundamental Theorem for Locally Ramified Domains 179
6.3. Appendix 1 196
6.4. Appendix 2 200
Chapter 7. Analytic Sets and Holomorphic Functions 209
7.1. Holomorphic Functions on Analytic Sets 209
7.2. Universal Denominators 215
7.3. £ Modules 220
7.4. Combination Theorems 231
7.5. Local Finiteness Theorem 251
Chapter 8. Analytic Spaces 267
8.1. Analytic Spaces 267
8.2. Analytic Polyhedra 270
8.3. Stein Spaces 280
8.4. Quantitative Estimates 291
8.5. Representation of a Stein space 301
8.6. Appendix 316
Chapter 9. Normal Pseudoconvex Spaces 321
9.1. Normal Pseudoconvex Spaces 321
9.2. Linking Problem 328
9.3. Principal Theorem 339
9.4. Unramified Domains Over Cn 344
Bibliography 359
Index 363
|
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| dewey-sort | 3515 294 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV014609125 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:19Z |
| institution | BVB |
| isbn | 0821808168 |
| language | English |
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| oclc_num | 248026266 |
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| owner_facet | DE-703 DE-11 |
| physical | XIII, 366 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Nishino, Toshio Verfasser aut Tahensu kansuron Function theory in several complex variables Toshio Nishino Providence, RI American Math. Soc. 2001 XIII, 366 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 193 Aus dem Japan. übers. Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s DE-604 Translations of mathematical monographs 193 (DE-604)BV000002394 193 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009930995&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nishino, Toshio Function theory in several complex variables Translations of mathematical monographs Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4277015-4 |
| title | Function theory in several complex variables |
| title_alt | Tahensu kansuron |
| title_auth | Function theory in several complex variables |
| title_exact_search | Function theory in several complex variables |
| title_full | Function theory in several complex variables Toshio Nishino |
| title_fullStr | Function theory in several complex variables Toshio Nishino |
| title_full_unstemmed | Function theory in several complex variables Toshio Nishino |
| title_short | Function theory in several complex variables |
| title_sort | function theory in several complex variables |
| topic | Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Funktionentheorie Mehrere Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009930995&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT nishinotoshio tahensukansuron AT nishinotoshio functiontheoryinseveralcomplexvariables |