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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Several Complex Variables (Paperback, Softcover reprint of the original 1st ed. 1976)
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Several Complex Variables (Paperback, Softcover reprint of the original 1st ed. 1976)
Series: Graduate Texts in Mathematics, 38
Expected to ship within 10 - 15 working days
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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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