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# đź“™ Analytic Function Theory of Several Variables: Elements of Okaâ€™s Coherence by Junjiro Noguchi (auth.) â€” free pdf

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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 Grauertâ€“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); Okaâ€“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 Cartanâ€“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:
**Junjiro Noguchi (auth.)** - Year:
**2016** - Publisher:
**Springer Singapore** - Language:
**English** - ISBN:
**978-981-10-0289-2,978-981-10-0291-5**

- File size:
**4 964 835** - Format:
**pdf**

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This book is an exposition of selected topics from the calculus of functions of several variables. It is intended for undergraduate mathematics stu- dents in the third or fourth year analysis program, who have had several semesters of the calculus a...

This text introduces basic ideas, structures, and results of differential and integral calculus for functions of several variables. The presentation is engaging and motivates the reader with numerous examples, remarks, illustrations, and exercises.Mathema...

This text introduces basic ideas, structures, and results of differential and integral calculus for functions of several variables. The presentation is engaging and motivates the reader with numerous examples, remarks, illustrations, and exercises.Mathema...

Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volum...

Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volum...

Second Edition. This famous work is a textbook that emphasizes the conceptual and historical continuity of analytic function theory. The second volume broadens from a textbook to a textbook-treatise, covering the ``canonical'' topics (including elliptic f...

The new edition of Function of Several Variables is an extensive revision. Like the first edition it presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. A new chapter ...

The general principles by which the editors and authors of the present edition have been guided were explained in the preface to the first volume of MathematÂ ics of the 19th Century, which contains chapters on the history of mathematical logic, algebra, ...

This is an expanded English-language version of a book by the same authors that originally appeared in the Japanese. The book serves two purposes. The first is to provide a self-contained and coherent account of recent developments in geometric function t...