Entire Functions Of Several Complex Variables
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Entire Functions Of Several Complex Variables
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Author : Pierre Lelong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Entire Functions Of Several Complex Variables written by Pierre Lelong 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.
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.
Introduction To The Theory Of Entire Functions Of Several Variables
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Author : Lev Isaakovich Ronkin
language : en
Publisher: American Mathematical Soc.
Release Date : 1974
Introduction To The Theory Of Entire Functions Of Several Variables written by Lev Isaakovich Ronkin 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 1974 with Mathematics categories.
Several Complex Variables Iii
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Author : G.M. Khenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Several Complex Variables Iii written by G.M. Khenkin 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.
We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space
Analytic Functions Of Several Complex Variables
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Author : Robert C. Gunning
language : en
Publisher: American Mathematical Society
Release Date : 2022-08-25
Analytic Functions Of Several Complex Variables written by Robert C. Gunning and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-25 with Mathematics categories.
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/publications/authors/books/postpub/chel-368.
Analytic Functions Of Several Complex Variables
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Author : Robert Clifford Gunning
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Analytic Functions Of Several Complex Variables written by Robert Clifford Gunning 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 2009 with Functional analysis categories.
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.
The Generalized Relative Gol Dberg Order And Type Some Remarks On Functions Of Complex Variables
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Author : Tanmay Biswas
language : en
Publisher: Bentham Science Publishers
Release Date : 2021-07-07
The Generalized Relative Gol Dberg Order And Type Some Remarks On Functions Of Complex Variables written by Tanmay Biswas and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-07 with Mathematics categories.
In The Generalized Relative Gol‘dberg Order and Type: Some Remarks on Functions of Complex Variables, the authors have discussed the generalized comparative growth analysis of entire functions of several complex variables at length. The discussion covers the important branch of complex analysis specially the theory of analytic functions of several variables. The book contains eight chapters. Chapter 1 presents introductory aspects of the topic and some preliminary definitions. In the proceeding chapters (2-8), the authors derive some results about the generalized Gol'dberg order (α,β) and generalized Gol'dberg type (α,β) of entire functions of several complex variables which progressively explores different variations of these variables, (upper and lower, functions, inequalities, growth measures). The book culminates in an explanation of the sum and product theorems depending on the generalized relative Gol'dberg order (α,β). This monograph is intended for mathematical researchers and enthusiasts who wish to expand their understanding about complex variables of several functions and complex and related aspects of complex analysis.
Function Theory Of Several Complex Variables
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Author : Steven George Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Function Theory Of Several Complex Variables written by Steven George Krantz 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 2001 with Functions of several complex variables categories.
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.
Several Complex Variables Iv
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Author : Semen G. Gindikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Several Complex Variables Iv written by Semen G. Gindikin 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.
This volume of the EMS contains four survey articles on analytic spaces. They are excellent introductions to each respective area. Starting from basic principles in several complex variables each article stretches out to current trends in research. Graduate students and researchers will find a useful addition in the extensive bibliography at the end of each article.
Holomorphic Functions And Integral Representations In Several Complex Variables
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Author : R. Michael Range
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Holomorphic Functions And Integral Representations In Several Complex Variables written by R. Michael Range 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 2013-03-09 with Mathematics categories.
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.
Tasty Bits Of Several Complex Variables
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Author : Jiri Lebl
language : en
Publisher: Lulu.com
Release Date : 2019-05-06
Tasty Bits Of Several Complex Variables written by Jiri Lebl and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-06 with categories.
An introduction to the field of Several Complex Variables. A course for graduate students after one semester of standard complex analysis in one variable. This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014, Spring 2016, and Spring 2019 semesters at Oklahoma State University. See https: //www.jirka.org/scv/ for more information.