Several Complex Variables

Name: Several Complex Variables
Brand: Springer, Berlin
SKU: 9781461298762
Price: 470.54 RON
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Autor: H. Grauert, K. Fritzsche

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Editura: Springer, Berlin

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The present book grew out of introductory lectures on the theory offunctions of several variables. I...

Informații despre carte

Autor

H. Grauert, K. Fritzsche

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2011

Pagini

208

EAN

9781461298762

ISBN

1461298768

Enbook ID

02180189

Editura

Springer, Berlin

Greutate

343

Dimensiuni

165 x 237 x 12

Descriere completă

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 contrast 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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Several Complex Variables

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