Several Complex Variables:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
New York, NY
Springer New York
1976
|
Schriftenreihe: | Graduate Texts in Mathematics
38 |
Schlagworte: | |
Online-Zugang: | Volltext |
Beschreibung: | The present book grew out of introductory lectures on the theory offunctions of several variables. Its intent is to make the reader familiar, by the discussion of examples and special cases, with the most important branches and methods of this theory, among them, e.g., the problems of holomorphic continuation, the algebraic treatment of power series, sheaf and cohomology theory, and the real methods which stem from elliptic partial differential equations. In the first chapter we begin with the definition of holomorphic functions of several variables, their representation by the Cauchy integral, and their power series expansion on Reinhardt domains. It turns out that, in l:ontrast ~ 2 there exist domains G, G c en to the theory of a single variable, for n with G c G and G "# G such that each function holomorphic in G has a continuation on G. Domains G for which such a G does not exist are called domains of holomorphy. In Chapter 2 we give several characterizations of these domains of holomorphy (theorem of Cartan-Thullen, Levi's problem). We finally construct the holomorphic hull H(G} for each domain G, that is the largest (not necessarily schlicht) domain over en into which each function holomorphic on G can be continued |
Beschreibung: | 1 Online-Ressource (VIII, 208 p) |
ISBN: | 9781461298748 9781461298762 |
ISSN: | 0072-5285 |
DOI: | 10.1007/978-1-4612-9874-8 |
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500 | |a The present book grew out of introductory lectures on the theory offunctions of several variables. Its intent is to make the reader familiar, by the discussion of examples and special cases, with the most important branches and methods of this theory, among them, e.g., the problems of holomorphic continuation, the algebraic treatment of power series, sheaf and cohomology theory, and the real methods which stem from elliptic partial differential equations. In the first chapter we begin with the definition of holomorphic functions of several variables, their representation by the Cauchy integral, and their power series expansion on Reinhardt domains. It turns out that, in l:ontrast ~ 2 there exist domains G, G c en to the theory of a single variable, for n with G c G and G "# G such that each function holomorphic in G has a continuation on G. Domains G for which such a G does not exist are called domains of holomorphy. In Chapter 2 we give several characterizations of these domains of holomorphy (theorem of Cartan-Thullen, Levi's problem). We finally construct the holomorphic hull H(G} for each domain G, that is the largest (not necessarily schlicht) domain over en into which each function holomorphic on G can be continued | ||
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Datensatz im Suchindex
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any_adam_object | |
author | Grauert, H. |
author_facet | Grauert, H. |
author_role | aut |
author_sort | Grauert, H. |
author_variant | h g hg |
building | Verbundindex |
bvnumber | BV042420494 |
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collection | ZDB-2-SMA ZDB-2-BAE |
ctrlnum | (OCoLC)863785854 (DE-599)BVBBV042420494 |
dewey-full | 510 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 510 - Mathematics |
dewey-raw | 510 |
dewey-search | 510 |
dewey-sort | 3510 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
doi_str_mv | 10.1007/978-1-4612-9874-8 |
format | Electronic eBook |
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id | DE-604.BV042420494 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T01:21:07Z |
institution | BVB |
isbn | 9781461298748 9781461298762 |
issn | 0072-5285 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855911 |
oclc_num | 863785854 |
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physical | 1 Online-Ressource (VIII, 208 p) |
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publishDate | 1976 |
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publisher | Springer New York |
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series2 | Graduate Texts in Mathematics |
spelling | Grauert, H. Verfasser aut Several Complex Variables edited by H. Grauert, K. Fritzsche New York, NY Springer New York 1976 1 Online-Ressource (VIII, 208 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 38 0072-5285 The present book grew out of introductory lectures on the theory offunctions of several variables. Its intent is to make the reader familiar, by the discussion of examples and special cases, with the most important branches and methods of this theory, among them, e.g., the problems of holomorphic continuation, the algebraic treatment of power series, sheaf and cohomology theory, and the real methods which stem from elliptic partial differential equations. In the first chapter we begin with the definition of holomorphic functions of several variables, their representation by the Cauchy integral, and their power series expansion on Reinhardt domains. It turns out that, in l:ontrast ~ 2 there exist domains G, G c en to the theory of a single variable, for n with G c G and G "# G such that each function holomorphic in G has a continuation on G. Domains G for which such a G does not exist are called domains of holomorphy. In Chapter 2 we give several characterizations of these domains of holomorphy (theorem of Cartan-Thullen, Levi's problem). We finally construct the holomorphic hull H(G} for each domain G, that is the largest (not necessarily schlicht) domain over en into which each function holomorphic on G can be continued Mathematics Mathematics, general Mathematik 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 Fritzsche, K. Sonstige oth Erscheint auch als Druck-Ausgabe 0-387-90172-8 https://doi.org/10.1007/978-1-4612-9874-8 Verlag Volltext |
spellingShingle | Grauert, H. Several Complex Variables Mathematics Mathematics, general Mathematik Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd |
subject_GND | (DE-588)4018935-1 (DE-588)4277015-4 |
title | Several Complex Variables |
title_auth | Several Complex Variables |
title_exact_search | Several Complex Variables |
title_full | Several Complex Variables edited by H. Grauert, K. Fritzsche |
title_fullStr | Several Complex Variables edited by H. Grauert, K. Fritzsche |
title_full_unstemmed | Several Complex Variables edited by H. Grauert, K. Fritzsche |
title_short | Several Complex Variables |
title_sort | several complex variables |
topic | Mathematics Mathematics, general Mathematik Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd |
topic_facet | Mathematics Mathematics, general Mathematik Funktionentheorie Mehrere Variable |
url | https://doi.org/10.1007/978-1-4612-9874-8 |
work_keys_str_mv | AT grauerth severalcomplexvariables AT fritzschek severalcomplexvariables |