lectures on several complex variables

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Lectures On Several Complex Variables

Author : Paul M. Gauthier
ISBN : 9783319115115
Genre : Mathematics
File Size : 45. 92 MB
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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.

Introduction To Several Complex Variables

Author : Lipman Bers
ISBN : PSU:000003378281
Genre : Mathematics
File Size : 49. 39 MB
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Lectures On Counterexamples In Several Complex Variables

Author : John Erik Fornæss
ISBN : 0821869493
Genre : Mathematics
File Size : 82. 36 MB
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Several Complex Variables

Author : Raghavan Narasimhan
ISBN : 0226568172
Genre : Mathematics
File Size : 37. 86 MB
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Drawn from lectures given by Raghavan Narasimhan at the University of Geneva and the University of Chicago, this book presents the part of the theory of several complex variables pertaining to unramified domains over C . Topics discussed are Hartogs' theory, domains in holomorphy, and automorphism of bounded domains.

Lectures On Several Complex Variables

Author : Yitzhak Katznelson
ISBN : OCLC:1049388004
Genre : Functions of complex variables
File Size : 51. 79 MB
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Lectures On Functions Of Several Complex Variables

Author : Lars Hörmander
ISBN : STANFORD:36105033197729
Genre : Mathematics
File Size : 42. 95 MB
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Several Complex Variables

Author : H. Grauert
ISBN : 9781461298748
Genre : Mathematics
File Size : 50. 6 MB
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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.

Dynamics In Several Complex Variables

Author : John Erik Fornæss
ISBN : 9780821803172
Genre : Mathematics
File Size : 33. 70 MB
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This CBMS lecture series, held in Albany, New York in June 1994, aimed to introduce the audience to the literature on complex dynamics in higher dimension. Some of the lectures are updated versions of earlier lectures given jointly with Nessim Sibony in Montreal 1993. The author's intent in this book is to give an expansion of the Montreal lectures, basing complex dynamics in higher dimension systematically on pluripotential theory. These notes provide an easy-to-read introduction into the field, an introduction that motivates the topics. The monograph then points readers towards technically more advanced literature.

Lectures On The Theory Of Functions Of Several Complex Variables

Author : Bernard Malgrange
ISBN : OCLC:17424913
Genre : Functions of several complex variables
File Size : 67. 29 MB
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Lectures On Several Complex Variables Notes Prepared By Frederick Greenleaf With The Assistance Of Matthew Rosenblatt Carruth Macgeehee I David Berg

Author : Yitzhak Katznelson
ISBN : OCLC:639846972
Genre : Functions of complex variables
File Size : 48. 68 MB
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