Analytic Function Theory Of Several Variables
DOWNLOAD
Download Analytic Function Theory Of Several Variables PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Analytic Function Theory Of Several Variables book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Analytic Function Theory Of Several Variables
DOWNLOAD
Author : Junjiro Noguchi
language : en
Publisher: Springer
Release Date : 2018-06-15
Analytic Function Theory Of Several Variables written by Junjiro Noguchi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-15 with Mathematics categories.
The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps).The core of the theory is "Oka's Coherence", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka's First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appears much later.The present book, consisting of nine chapters, gives complete treatments of the following items: Coherence of sheaves of holomorphic functions (Chap. 2); Oka–Cartan's Fundamental Theorem (Chap. 4); Coherence of ideal sheaves of complex analytic subsets (Chap. 6); Coherence of the normalization sheaves of complex spaces (Chap. 6); Grauert's Finiteness Theorem (Chaps. 7, 8); Oka's Theorem for Riemann domains (Chap. 8). The theories of sheaf cohomology and domains of holomorphy are also presented (Chaps. 3, 5). Chapter 6 deals with the theory of complex analytic subsets. Chapter 8 is devoted to the applications of formerly obtained results, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. 9, we discuss the historical development of "Coherence".It is difficult to find a book at this level that treats all of the above subjects in a completely self-contained manner. In the present volume, a number of classical proofs are improved and simplified, so that the contents are easily accessible for beginning graduate students.
Function Theory Of Several Complex Variables
DOWNLOAD
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.
Function Theory In Several Complex Variables
DOWNLOAD
Author : Toshio Nishino
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Function Theory In Several Complex Variables written by Toshio Nishino 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 Mathematics categories.
'Kiyoshi Oka, at the beginning of his research, regarded the collection of problems which he encountered in the study of domains of holomorphy as large mountains which separate today and tomorrow. Thus, he believed that there could be no essential progress in analysis without climbing over these mountains ... this book is a worthwhile initial step for the reader in order to understand the mathematical world which was created by Kiyoshi Oka.' -- from the Preface. This book explains results in the theory of functions of several complex variables which were mostly established from the late nineteenth century through to the middle of the twentieth century. In the work, the author introduces the mathematical world created by his advisor, Kiyoshi Oka. In this volume, Oka's work is divided into two parts. The first is the study of analytic functions in univalent domains in ${\mathbf C}n$. Here Oka proved that three concepts are equivalent: domains of holomorphy, holomorphically convex domains, and pseudoconvex domains; and moreover that the Poincaré problem, the Cousin problems, and the Runge problem, when stated properly, can be solved in domains of holomorphy satisfying the appropriate conditions. The second part of Oka's work established a method for the study of analytic functions defined in a ramified domain over ${\mathbf C}n$ in which the branch points are considered as interior points of the domain. Here analytic functions in an analytic space are treated, which is a slight generalization of a ramified domain over ${\mathbf C}n$. In writing the book, the author's goal was to bring to readers a real understanding of Oka's original papers. This volume is an English translation of the original Japanese edition, published by the University of Tokyo Press (Japan). It would make a suitable course text for advanced graduate level introductions to several complex variables.
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables
DOWNLOAD
Author : Henri Cartan
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables written by Henri Cartan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
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.
Special Chapters In The Theory Of Analytic Functions Of Several Complex Variables
DOWNLOAD
Author : B. A. Fuks
language : en
Publisher: American Mathematical Soc.
Release Date : 1965-12-31
Special Chapters In The Theory Of Analytic Functions Of Several Complex Variables written by B. A. Fuks 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 1965-12-31 with Mathematics categories.
Analytic Functions Of Several Complex Variables
DOWNLOAD
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.
Theory Of Analytic Functions Of Several Complex Variables
DOWNLOAD
Author : Boris Abramovich Fuks
language : en
Publisher: American Mathematical Soc.
Release Date : 1963
Theory Of Analytic Functions Of Several Complex Variables written by Boris Abramovich Fuks 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 1963 with Mathematics categories.
Introduction To The Theory Of Analytic Functions Of Several Complex Variables
DOWNLOAD
Author : Boris A. Fuks
language : en
Publisher:
Release Date : 1965
Introduction To The Theory Of Analytic Functions Of Several Complex Variables written by Boris A. Fuks and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Functions of complex variables categories.
Analytic Function Theory Of One Complex Variable
DOWNLOAD
Author : Yūsaku Komatsu
language : en
Publisher: Longman
Release Date : 1989
Analytic Function Theory Of One Complex Variable written by Yūsaku Komatsu and has been published by Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Analytic functions categories.
Introduction To The Theory Of Analytic Functions Of Several Complex Variables
DOWNLOAD
Author : B. A. Fuks
language : en
Publisher:
Release Date : 1963
Introduction To The Theory Of Analytic Functions Of Several Complex Variables written by B. A. Fuks and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Analytic functions categories.