DMCA. Copyrighted Work that you can Claim.
Base have 820 524 books.
Search: 


📙 Analytic Function Theory of Several Variables: Elements of Oka’s Coherence by Junjiro Noguchi (auth.) — free pdf


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.



About book:

About file:

  • File size: 4 964 835
  • Format: pdf


Security code:
Download button

Similar books results


Functions of Several Variables
Functions of Several Variables download pdf by John W. Woll

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...

Mathematical Analysis: An Introduction to Functions of Several Variables
Mathematical Analysis: An Introduction to Functions of Several Variables pdf free by Mariano Giaquinta, Giuseppe Modica (auth.)

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: An introduction to functions of several variables
Mathematical analysis: An introduction to functions of several variables download pdf by Mariano Giaquinta, Giuseppe Modica (auth.)

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
Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables free pdf by Mariano Giaquinta, Giuseppe Modica (auth.)

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
Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables epub download by Mariano Giaquinta, Giuseppe Modica (auth.)

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...

Analytic function theory
Analytic function theory (Volume 1) pdf free by Einar Hille

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...

Functions of Several Variables
Functions of Several Variables free pdf by Wendell Fleming

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 ...

Mathematics of the 19th Century: Geometry, Analytic Function Theory
Mathematics of the 19th Century: Geometry, Analytic Function Theory free pdf by B. L. Laptev, B. A. Rozenfel’d (auth.), A. N. Kolmogorov, A. P. Yushkevich (eds.)

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 Mathemat­ ics of the 19th Century, which contains chapters on the history of mathematical logic, algebra, ...

Geometric Function Theory in Several Complex Variables
Geometric Function Theory in Several Complex Variables free pdf by Junjiro Noguchi and Takushiro Ochiai

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...