Special Chapters In The Theory Of Analytic Functions Of Several Complex Variables
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Special Chapters In The Theory Of Analytic Functions Of Several Complex Variables
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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.
Special Chapters In The Theory Of Analytic Functions Of Several Complex Variables
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Author : B.A. Fuks
language : en
Publisher:
Release Date : 1956
Special Chapters In 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 1956 with categories.
Special Chapters In The Theory Of Analytic Functions Of Several Complex Variables
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Author : B. A. Fuchs
language : en
Publisher:
Release Date : 1965
Special Chapters In The Theory Of Analytic Functions Of Several Complex Variables written by B. A. Fuchs 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.
Theory Of Analytic Functions Of Several Complex Variables
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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
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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.
Introduction To The Theory Of Analytic Functions Of Several Complex Variables
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Author : Boris Abramovich Fuks
language : en
Publisher:
Release Date : 1963
Introduction To The Theory Of Analytic Functions Of Several Complex Variables written by Boris Abramovich 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 Functions of complex variables categories.
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.
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables
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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.
Analytic Function Theory Of Several Variables
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Author : Junjiro Noguchi
language : en
Publisher: Springer
Release Date : 2016-08-16
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 2016-08-16 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.
Complex Analysis
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Author : John Stalker
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03
Complex Analysis written by John Stalker 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 2009-10-03 with Mathematics categories.
All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75]. In "part I'' we find the foundational material, the basic definitions and theorems. In "part II" we find the examples and applications. Slowly we begin to understand why we read part I. Historically this is an anachronism. Pedagogically it is a disaster. Part II in fact predates part I, so clearly it can be taught first. Why should the student have to wade through hundreds of pages before finding out what the subject is good for? In teaching complex analysis this way, we risk more than just boredom. Beginning with a series of unmotivated definitions gives a misleading impression of complex analy sis in particular and of mathematics in general. The classical theory of analytic functions did not arise from the idle speculation of bored mathematicians on the possible conse quences of an arbitrary set of definitions; it was the natural, even inevitable, consequence of the practical need to answer questions about specific examples. In standard texts, after hundreds of pages of theorems about generic analytic functions with only the rational and trigonometric functions as examples, students inevitably begin to believe that the purpose of complex analysis is to produce more such theorems. We require introductory com plex analysis courses of our undergraduates and graduates because it is useful both within mathematics and beyond.