Analytic Function Theory of Several Variables

Elements of Oka’s Coherence

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Algebra
Cover of the book Analytic Function Theory of Several Variables by Junjiro Noguchi, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Junjiro Noguchi ISBN: 9789811002915
Publisher: Springer Singapore Publication: August 16, 2016
Imprint: Springer Language: English
Author: Junjiro Noguchi
ISBN: 9789811002915
Publisher: Springer Singapore
Publication: August 16, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Singapore

Cover of the book Modern China’s Copyright Law and Practice by Junjiro Noguchi
Cover of the book Advanced Detectors for Nuclear, High Energy and Astroparticle Physics by Junjiro Noguchi
Cover of the book A DIY Guide to Telemedicine for Clinicians by Junjiro Noguchi
Cover of the book Education in Japan by Junjiro Noguchi
Cover of the book Theoretical and Experimental Aerodynamics by Junjiro Noguchi
Cover of the book Development of a Fully Integrated “Sample-In-Answer-Out” System for Automatic Genetic Analysis by Junjiro Noguchi
Cover of the book Distributed Fusion Estimation for Sensor Networks with Communication Constraints by Junjiro Noguchi
Cover of the book Basic and Applied Phytoplankton Biology by Junjiro Noguchi
Cover of the book Doubly Classified Model with R by Junjiro Noguchi
Cover of the book At Home with Democracy by Junjiro Noguchi
Cover of the book Advances in Communication, Cloud, and Big Data by Junjiro Noguchi
Cover of the book Permanent Magnet Spherical Motors by Junjiro Noguchi
Cover of the book Research on Ship Design and Optimization Based on Simulation-Based Design (SBD) Technique by Junjiro Noguchi
Cover of the book Educational Researchers and the Regional University by Junjiro Noguchi
Cover of the book A Course in BE-algebras by Junjiro Noguchi
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy