Lectures on the theory of functions of a complex variable PDF Download

Author:
Publisher:
ISBN:
Category : Functions of complex variables
Languages : en
Pages : 488

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Author: Giovanni Sansone
Publisher:
ISBN:
Category : Functions of complex variables
Languages : en
Pages : 488

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Author: Bernard Malgrange
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 146

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Author: G. Sansone
Publisher: Springer
ISBN: 9789028609044
Category : Mathematics
Languages : en
Pages : 1188

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Author: George Whitelaw Mackey
Publisher: Krieger Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 284

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Author: Paul M. Gauthier
Publisher: Springer
ISBN: 3319115111
Category : Mathematics
Languages : en
Pages : 110

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​​​This monograph provides a concise, accessible snapshot of key topics in several complex variables, including the Cauchy Integral Formula, sequences of holomorphic functions, plurisubharmonic functions, the Dirichlet problem, and meromorphic functions. Based on a course given at Université de Montréal, this brief introduction covers areas of contemporary importance that are not mentioned in most treatments of the subject, such as modular forms, which are essential for Wiles' theorem and the unification of quantum theory and general relativity. Also covered is the Riemann manifold of a function, which generalizes the Riemann surface of a function of a single complex variable and is a topic that is well-known in one complex variable, but rarely treated in several variables. Many details, which are intentionally left out, as well as many theorems are stated as problems, providing students with carefully structured instructive exercises. Prerequisites for use of this book are functions of one complex variable, functions of several real variables, and topology, all at the undergraduate level. Lectures on Several Complex Variables will be of interest to advanced undergraduate and beginning undergraduate students, as well as mathematical researchers and professors.

Author: Giovanni Sansone
Publisher:
ISBN:
Category : Functions of complex variables
Languages : en
Pages : 720

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Author: Wilfred Kaplan
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 456

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Author: H. Grauert
Publisher: Springer Science & Business Media
ISBN: 1461298741
Category : Mathematics
Languages : en
Pages : 213

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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.

Author: Giovanni Sansone
Publisher:
ISBN:
Category :
Languages : en
Pages :

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