[PDF] Functions Of Several Complex Variables And Their Singularities eBook

Author : Wolfgang Ebeling
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 35,89 MB
Release : 2007
Category : Mathematics
ISBN : 0821833197

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The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.

Author : Robert Clifford Gunning
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 36,38 MB
Release : 2009
Category : Mathematics
ISBN : 0821821652

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The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.

Author : Pierre Lelong
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 22,59 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642703445

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I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.

Author : Henri Cartan
Publisher : Courier Corporation
Page : 242 pages
File Size : 46,48 MB
Release : 2013-04-22
Category : Mathematics
ISBN : 0486318672

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Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.

Author : Alekseĭ Georgievich Sveshnikov
Publisher :
Page : 344 pages
File Size : 50,77 MB
Release : 1978
Category : Functions of complex variables
ISBN :

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The complex variable and functions of a complex variable; Series of analytical functions; Analytic continuation elementary; The laurent series and isolated singular points; Residues and their applications; Conformal mapping; Analytic-functions in the solutions of boundary-value problems; Fundamentals of operational calculus; Saddle-point method; The wiener-hopf method; Functions of many complex variables.

Author : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 33,51 MB
Release : 2001
Category : Mathematics
ISBN : 0821827243

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Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.