Introduction To The Theory Of Analytic Functions Of Several Complex Variables PDF Download
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Author | : Robert C. Gunning |
Publisher | : American Mathematical Society |
Total Pages | : 334 |
Release | : 2022-08-25 |
Genre | : Mathematics |
ISBN | : 1470470667 |
Download Analytic Functions of Several Complex Variables Book in PDF, ePub and Kindle
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.
Author | : Henri Cartan |
Publisher | : Courier Corporation |
Total Pages | : 242 |
Release | : 2013-04-22 |
Genre | : Mathematics |
ISBN | : 0486318672 |
Download Elementary Theory of Analytic Functions of One or Several Complex Variables Book in PDF, ePub and Kindle
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.
Author | : Boris A. Fuks |
Publisher | : |
Total Pages | : 412 |
Release | : 1965 |
Genre | : Functions of complex variables |
ISBN | : |
Download Introduction to the Theory of Analytic Functions of Several Complex Variables Book in PDF, ePub and Kindle
Author | : Steven George Krantz |
Publisher | : American Mathematical Soc. |
Total Pages | : 586 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821827243 |
Download Function Theory of Several Complex Variables Book in PDF, ePub and Kindle
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 | : Boris Abramovich Fuks |
Publisher | : |
Total Pages | : |
Release | : 1963 |
Genre | : Functions of complex variables |
ISBN | : |
Download Introduction to the Theory of Analytic Functions of Several Complex Variables Book in PDF, ePub and Kindle
Author | : Vasiliy Sergeyevich Vladimirov |
Publisher | : Courier Corporation |
Total Pages | : 370 |
Release | : 2007-01-01 |
Genre | : Mathematics |
ISBN | : 0486458121 |
Download Methods of the Theory of Functions of Many Complex Variables Book in PDF, ePub and Kindle
This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.
Author | : B. A. Fuks |
Publisher | : American Mathematical Soc. |
Total Pages | : 366 |
Release | : 1965-12-31 |
Genre | : Mathematics |
ISBN | : 0821815644 |
Download Special Chapters in the Theory of Analytic Functions of Several Complex Variables Book in PDF, ePub and Kindle
Author | : Boris Abramovich Fuks |
Publisher | : American Mathematical Soc. |
Total Pages | : 402 |
Release | : 1963 |
Genre | : Mathematics |
ISBN | : 9780821886441 |
Download Theory of Analytic Functions of Several Complex Variables Book in PDF, ePub and Kindle
Author | : Junjiro Noguchi |
Publisher | : Springer |
Total Pages | : 407 |
Release | : 2016-08-16 |
Genre | : Mathematics |
ISBN | : 9811002916 |
Download Analytic Function Theory of Several Variables Book in PDF, ePub and Kindle
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.
Author | : FUKS B.A. |
Publisher | : |
Total Pages | : 0 |
Release | : 1963 |
Genre | : |
ISBN | : |
Download Introduction to the theory of analytic functions of several complex variables Book in PDF, ePub and Kindle