Softcover ISBN:  9780821820988 
Product Code:  MMONO/211 
List Price:  $40.00 
MAA Member Price:  $36.00 
AMS Member Price:  $32.00 
Electronic ISBN:  9781470446369 
Product Code:  MMONO/211.E 
List Price:  $37.00 
MAA Member Price:  $33.30 
AMS Member Price:  $29.60 

Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 211; 2002; 121 ppMSC: Primary 32;
One of the approaches to the study of functions of several complex variables is to use methods originating in real analysis. In this concise book, the author gives a lucid presentation of how these methods produce a variety of global existence theorems in the theory of functions (based on the characterization of holomorphic functions as weak solutions of the CauchyRiemann equations).
Emphasis is on recent results, including an \(L^2\) extension theorem for holomorphic functions, that have brought a deeper understanding of pseudoconvexity and plurisubharmonic functions. Based on Oka's theorems and his schema for the grouping of problems, the book covers topics at the intersection of the theory of analytic functions of several variables and mathematical analysis.
It is assumed that the reader has a basic knowledge of complex analysis at the undergraduate level. The book would make a fine supplementary text for a graduatelevel course on complex analysis.ReadershipGraduate students and research mathematicians interested in several complex variables and analytic spaces.

Table of Contents

Chapters

Holomorphic functions

Rings of holomorphic functions and $\overline {\partial }$ cohomology

Pseudoconvexity and plurisubharmonic functions

$L^2$ estimates and existence theorems

Solutions of the extension and division problems

Bergman kernels


Reviews

The goal of this admirable little book is … to ascend rapidly to a few wellchosen peaks.
Mathematical Reviews 
Concise booklet … The author gives a lucid presentation … The book would make a fine supplementary text for a graduatelevel course on complex analysis.
Zentralblatt MATH


Request Review Copy

Get Permissions
 Book Details
 Table of Contents
 Reviews

 Request Review Copy
 Get Permissions
One of the approaches to the study of functions of several complex variables is to use methods originating in real analysis. In this concise book, the author gives a lucid presentation of how these methods produce a variety of global existence theorems in the theory of functions (based on the characterization of holomorphic functions as weak solutions of the CauchyRiemann equations).
Emphasis is on recent results, including an \(L^2\) extension theorem for holomorphic functions, that have brought a deeper understanding of pseudoconvexity and plurisubharmonic functions. Based on Oka's theorems and his schema for the grouping of problems, the book covers topics at the intersection of the theory of analytic functions of several variables and mathematical analysis.
It is assumed that the reader has a basic knowledge of complex analysis at the undergraduate level. The book would make a fine supplementary text for a graduatelevel course on complex analysis.
Graduate students and research mathematicians interested in several complex variables and analytic spaces.

Chapters

Holomorphic functions

Rings of holomorphic functions and $\overline {\partial }$ cohomology

Pseudoconvexity and plurisubharmonic functions

$L^2$ estimates and existence theorems

Solutions of the extension and division problems

Bergman kernels

The goal of this admirable little book is … to ascend rapidly to a few wellchosen peaks.
Mathematical Reviews 
Concise booklet … The author gives a lucid presentation … The book would make a fine supplementary text for a graduatelevel course on complex analysis.
Zentralblatt MATH