First steps in several complex variables: Reinhardt domains
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Zürich
European Mathematical Society
[2008]
|
| Schriftenreihe: | EMS Textbooks in athematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | viii, 359 Seiten Diagramme |
| ISBN: | 3037190493 9783037190494 |
Internformat
MARC
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| 245 | 1 | 0 | |a First steps in several complex variables |b Reinhardt domains |c Marek Jarnicki, Peter Pflug |
| 264 | 1 | |a Zürich |b European Mathematical Society |c [2008] | |
| 264 | 4 | |c © 2008 | |
| 300 | |a viii, 359 Seiten |b Diagramme | ||
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Datensatz im Suchindex
| _version_ | 1804137962356604928 |
|---|---|
| adam_text | Contents
Preface
v
1 Reinhardt
domains
1
1.1
Introduction
............................ 1
1.2
Summable families
......................... 6
1.3
Domains of convergence of power series
............. 13
1.4
Maximal
affine
subspace of a convex set I
............. 20
1.5 Reinhardt
domains
......................... 29
1.6
Domains of convergence of Laurent series
............ 41
1.7
Holomorphic functions
...................... 47
1.8
Balanced domains
......................... 55
1.9
Extension of holomorphic functions
................ 58
1.10
Natural
Fréchet
spaces
....................... 63
1.11
Domains of holomorphy
...................... 72
1.12
Envelopes of holomorphy
..................... 84
1.13
Holomorphic convexity
...................... 89
1.14
Plurisubharmonic functions
.................... 100
1.15
Pseudoconvexity
.......................... 117
1.16
Levi
problem
............................ 128
1.17
Hyperconvexity
.......................... 130
1.18*
Smooth pseudoconvex domains
.................. 142
1.19*
Complete
Kahler
metrics
..................... 146
2
Biholomorphisms of
Reinhardt
domains
160
2.1
Introduction
............................ 160
2.2*
Cartan theory
............................ 177
2.3
Biholomorphisms of bounded complete
Reinhardt
domains
inC2
................................ 180
2.4
Biholomorphisms of complete elementary
Reinhardt
domains
inC2
................................ 196
2.5*
Miscellanea
............................ 207
3 Reinhardt
domains of existence of special classes of holomorphic
functions
220
3.1
General theory
........................... 220
3.2
Elementary
Reinhardt
domains
.................. 225
3.3
Maximal
affine
subspace of a convex set II
............ 230
viii Contents
3.4
ЈЃ00
-domains
of holomorphy
................... 236
3.5
Afc-domains of holomorphy
.................... 239
3.6
L^-domains of holomorphy
.................... 241
4
Holomorphically contractible families on
Reinhardt
domains
251
4.1
Introduction
............................ 251
4.2
Holomorphically contractible families of functions
........ 253
4.3* Hahn
function
........................... 269
4.4
Examples I
-
elementary
Reinhardt
domains
........... 277
4.5
Holomorphically contractible families of pseudometrics
..... 293
4.6
Examples II
-
elementary
Reinhardt
domains
........... 310
4.7
Hyperbolic
Reinhardt
domains
.................. 313
4.8
Carathéodory (resp.
Kobayashi) complete
Reinhardt
domains
. . 317
4.9*
The Bergman completeness of
Reinhardt
domains
........ 325
Bibliography
333
Symbols
345
List of symbols
349
Subject index
355
|
| adam_txt |
Contents
Preface
v
1 Reinhardt
domains
1
1.1
Introduction
. 1
1.2
Summable families
. 6
1.3
Domains of convergence of power series
. 13
1.4
Maximal
affine
subspace of a convex set I
. 20
1.5 Reinhardt
domains
. 29
1.6
Domains of convergence of Laurent series
. 41
1.7
Holomorphic functions
. 47
1.8
Balanced domains
. 55
1.9
Extension of holomorphic functions
. 58
1.10
Natural
Fréchet
spaces
. 63
1.11
Domains of holomorphy
. 72
1.12
Envelopes of holomorphy
. 84
1.13
Holomorphic convexity
. 89
1.14
Plurisubharmonic functions
. 100
1.15
Pseudoconvexity
. 117
1.16
Levi
problem
. 128
1.17
Hyperconvexity
. 130
1.18*
Smooth pseudoconvex domains
. 142
1.19*
Complete
Kahler
metrics
. 146
2
Biholomorphisms of
Reinhardt
domains
160
2.1
Introduction
. 160
2.2*
Cartan theory
. 177
2.3
Biholomorphisms of bounded complete
Reinhardt
domains
inC2
. 180
2.4
Biholomorphisms of complete elementary
Reinhardt
domains
inC2
. 196
2.5*
Miscellanea
. 207
3 Reinhardt
domains of existence of special classes of holomorphic
functions
220
3.1
General theory
. 220
3.2
Elementary
Reinhardt
domains
. 225
3.3
Maximal
affine
subspace of a convex set II
. 230
viii Contents
3.4
ЈЃ00
-domains
of holomorphy
. 236
3.5
Afc-domains of holomorphy
. 239
3.6
L^-domains of holomorphy
. 241
4
Holomorphically contractible families on
Reinhardt
domains
251
4.1
Introduction
. 251
4.2
Holomorphically contractible families of functions
. 253
4.3* Hahn
function
. 269
4.4
Examples I
-
elementary
Reinhardt
domains
. 277
4.5
Holomorphically contractible families of pseudometrics
. 293
4.6
Examples II
-
elementary
Reinhardt
domains
. 310
4.7
Hyperbolic
Reinhardt
domains
. 313
4.8
Carathéodory (resp.
Kobayashi) complete
Reinhardt
domains
. . 317
4.9*
The Bergman completeness of
Reinhardt
domains
. 325
Bibliography
333
Symbols
345
List of symbols
349
Subject index
355 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:50:01Z |
| indexdate | 2024-07-09T21:20:37Z |
| institution | BVB |
| isbn | 3037190493 9783037190494 |
| language | English |
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| physical | viii, 359 Seiten Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | European Mathematical Society |
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| spelling | Jarnicki, Marek 1952- Verfasser (DE-588)101811095X aut First steps in several complex variables Reinhardt domains Marek Jarnicki, Peter Pflug Zürich European Mathematical Society [2008] © 2008 viii, 359 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier EMS Textbooks in athematics Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionentheorie (DE-588)4018935-1 s Mehrere komplexe Variable (DE-588)4169285-8 s DE-604 Pflug, Peter 1943- Sonstige (DE-588)1018111301 oth Erscheint auch als ebook Jarnicki, Marek First steps in several complex variables 978-3-03719-549-9 (DE-604)BV036713248 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016700603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jarnicki, Marek 1952- First steps in several complex variables Reinhardt domains Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4169285-8 (DE-588)4123623-3 |
| title | First steps in several complex variables Reinhardt domains |
| title_auth | First steps in several complex variables Reinhardt domains |
| title_exact_search | First steps in several complex variables Reinhardt domains |
| title_exact_search_txtP | First steps in several complex variables Reinhardt domains |
| title_full | First steps in several complex variables Reinhardt domains Marek Jarnicki, Peter Pflug |
| title_fullStr | First steps in several complex variables Reinhardt domains Marek Jarnicki, Peter Pflug |
| title_full_unstemmed | First steps in several complex variables Reinhardt domains Marek Jarnicki, Peter Pflug |
| title_short | First steps in several complex variables |
| title_sort | first steps in several complex variables reinhardt domains |
| title_sub | Reinhardt domains |
| topic | Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Funktionentheorie Mehrere komplexe Variable Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016700603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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