Several Complex Variables Ii
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Author |
: Robert Clifford Gunning |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 338 |
Release |
: 2009 |
ISBN-10 |
: 9780821821657 |
ISBN-13 |
: 0821821652 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Analytic Functions of Several Complex Variables by : Robert Clifford Gunning
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 |
: Eberhard Freitag |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 521 |
Release |
: 2011-06-10 |
ISBN-10 |
: 9783642205545 |
ISBN-13 |
: 3642205542 |
Rating |
: 4/5 (45 Downloads) |
Synopsis Complex Analysis 2 by : Eberhard Freitag
The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ̄rst volume. There is no comparable treatment in the literature.
Author |
: Pierre Lelong |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 283 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642703447 |
ISBN-13 |
: 3642703445 |
Rating |
: 4/5 (47 Downloads) |
Synopsis Entire Functions of Several Complex Variables by : Pierre Lelong
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 |
: R. Michael Range |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 405 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9781475719185 |
ISBN-13 |
: 1475719183 |
Rating |
: 4/5 (85 Downloads) |
Synopsis Holomorphic Functions and Integral Representations in Several Complex Variables by : R. Michael Range
The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
Author |
: H. Grauert |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 213 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461298748 |
ISBN-13 |
: 1461298741 |
Rating |
: 4/5 (48 Downloads) |
Synopsis Several Complex Variables by : H. Grauert
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 |
: Steven George Krantz |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 586 |
Release |
: 2001 |
ISBN-10 |
: 9780821827246 |
ISBN-13 |
: 0821827243 |
Rating |
: 4/5 (46 Downloads) |
Synopsis Function Theory of Several Complex Variables by : Steven George Krantz
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.
Author |
: Mike Field |
Publisher |
: Cambridge University Press |
Total Pages |
: 224 |
Release |
: 1982 |
ISBN-10 |
: 0521288886 |
ISBN-13 |
: 9780521288880 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Several Complex Variables and Complex Manifolds by : Mike Field
Annotation This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject.
Author |
: Wolfgang Ebeling |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 334 |
Release |
: 2007 |
ISBN-10 |
: 9780821833193 |
ISBN-13 |
: 0821833197 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Functions of Several Complex Variables and Their Singularities by : Wolfgang Ebeling
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 |
: Jiri Lebl |
Publisher |
: Lulu.com |
Total Pages |
: 142 |
Release |
: 2016-05-05 |
ISBN-10 |
: 9781365095573 |
ISBN-13 |
: 1365095576 |
Rating |
: 4/5 (73 Downloads) |
Synopsis Tasty Bits of Several Complex Variables by : Jiri Lebl
This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.
Author |
: G. M. Khenkin |
Publisher |
: Springer |
Total Pages |
: 280 |
Release |
: 1994 |
ISBN-10 |
: UCSD:31822016892804 |
ISBN-13 |
: |
Rating |
: 4/5 (04 Downloads) |
Synopsis Several Complex Variables II by : G. M. Khenkin
This volume of the Encyclopaedia contains four parts each of which being an informative survey of a topic in the field of several complex variables. Thefirst deals with residue theory and its applications to integrals depending on parameters, combinatorial sums and systems of algebraic equations. The second part contains recent results in complex potential theory and the third part treats function theory in the unit ball covering research of the last twenty years. The latter part includes an up-to-date account of research related to a list of problems, which was published by Rudin in 1980. The last part of the book treats complex analysis in the futuretube. The future tube is an important concept in mathematical physics, especially in axiomatic quantum field theory, and it is related to Penrose'swork on "the complex geometry of the real world". Researchers and graduate students in complex analysis and mathematical physics will use thisbook as a reference and as a guide to exciting areas of research.