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Lectures On Several Complex Variables


Lectures On Several Complex Variables
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Lectures On Several Complex Variables


Lectures On Several Complex Variables
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Author : Paul M. Gauthier
language : en
Publisher: Springer
Release Date : 2014-11-07

Lectures On Several Complex Variables written by Paul M. Gauthier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Mathematics categories.


​​​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.



Several Complex Variables


Several Complex Variables
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Author : Raghavan Narasimhan
language : en
Publisher: University of Chicago Press
Release Date : 1971

Several Complex Variables written by Raghavan Narasimhan and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.


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 The Theory Of Functions Of Several Complex Variables


Lectures On The Theory Of Functions Of Several Complex Variables
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Author : Bernard Malgrange
language : en
Publisher:
Release Date : 1984

Lectures On The Theory Of Functions Of Several Complex Variables written by Bernard Malgrange and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Functions of complex variables categories.




Several Complex Variables


Several Complex Variables
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Author : H. Grauert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Several Complex Variables written by H. Grauert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


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.



Lectures On Counterexamples In Several Complex Variables


Lectures On Counterexamples In Several Complex Variables
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Author : John Erik Fornæss
language : en
Publisher: American Mathematical Soc.
Release Date :

Lectures On Counterexamples In Several Complex Variables written by John Erik Fornæss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.


Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornaess and Stensones look at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations. The first part of the book reviews some of the basics of the theory, in a self-contained introduction to several complex variables. The counterexamples cover a variety of important topics: the Levi problem, plurisubharmonic functions, Monge-Ampere equations, CR geometry, function theory, and the $\bar\partial$ equation. The book would be an excellent supplement to a graduate course on several complex variables.



Twenty One Lectures On Complex Analysis


Twenty One Lectures On Complex Analysis
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Author : Alexander Isaev
language : en
Publisher: Springer
Release Date : 2017-11-29

Twenty One Lectures On Complex Analysis written by Alexander Isaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-29 with Mathematics categories.


At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student’s progression, more advanced topics are spread out over several lectures. This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy’s Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy’s Integral Theorem and Cauchy’s Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.



Dynamics In One Complex Variable


Dynamics In One Complex Variable
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Author : John Milnor
language : en
Publisher: Vieweg+teubner Verlag
Release Date : 2000-06-28

Dynamics In One Complex Variable written by John Milnor and has been published by Vieweg+teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-28 with Mathematics categories.


This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. The subject is large and rapidly growing. These notes are intended to introduce the reader to some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology.



Lecture Notes On Complex Analysis


Lecture Notes On Complex Analysis
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Author : Wilde Ivan Francis
language : en
Publisher: World Scientific
Release Date : 2006-04-11

Lecture Notes On Complex Analysis written by Wilde Ivan Francis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Mathematics categories.


This book is based on lectures presented over many years to second and third year mathematics students in the Mathematics Departments at Bedford College, London, and King's College, London, as part of the BSc. and MSci. program. Its aim is to provide a gentle yet rigorous first course on complex analysis.Metric space aspects of the complex plane are discussed in detail, making this text an excellent introduction to metric space theory. The complex exponential and trigonometric functions are defined from first principles and great care is taken to derive their familiar properties. In particular, the appearance of π, in this context, is carefully explained.The central results of the subject, such as Cauchy's Theorem and its immediate corollaries, as well as the theory of singularities and the Residue Theorem are carefully treated while avoiding overly complicated generality. Throughout, the theory is illustrated by examples.A number of relevant results from real analysis are collected, complete with proofs, in an appendix.The approach in this book attempts to soften the impact for the student who may feel less than completely comfortable with the logical but often overly concise presentation of mathematical analysis elsewhere.



Dynamics In Several Complex Variables


Dynamics In Several Complex Variables
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Author : John Erik Fornæss
language : en
Publisher: American Mathematical Soc.
Release Date :

Dynamics In Several Complex Variables written by John Erik Fornæss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.


This is part of the 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. These notes provide an easy to read introduction into the field. This monograph then points readers towards technically more advanced literature.



Analysis Of Several Complex Variables


Analysis Of Several Complex Variables
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Author : Takeo Ōsawa
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Analysis Of Several Complex Variables written by Takeo Ōsawa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.


An expository account of the basic results in several complex variables that are obtained by L℗ methods.