**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2002; 121 pp; Softcover

MSC: Primary 32;

Print ISBN: 978-0-8218-2098-8

Product Code: MMONO/211

Print ISBN: 978-0-8218-2098-8

Product Code: MMONO/211

List Price: $37.00

AMS Member Price: $29.60

MAA Member Price: $33.30

**Electronic ISBN: 978-1-4704-4636-9
Product Code: MMONO/211.E**

List Price: $37.00

AMS Member Price: $29.60

MAA Member Price: $33.30

# Analysis of Several Complex Variables

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*Takeo Ohsawa*

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 Cauchy-Riemann 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 graduate-level course on complex analysis.

#### Readership

Graduate students and research mathematicians interested in several complex variables and analytic spaces.

#### Reviews & Endorsements

The goal of this admirable little book is … to ascend rapidly to a few well-chosen peaks.

-- Mathematical Reviews

Concise booklet … The author gives a lucid presentation … The book would make a fine supplementary text for a graduate-level course on complex analysis.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Analysis of Several Complex Variables

- Cover Cover11
- Other title in this series i2
- Title page v6
- Contents vii8
- Preface ix10
- Preface to the English edition xi12
- Summary and prospects of the theory xiii14
- Holomorphic functions 120
- Rings of holomorphic functions and \overline{∂} cohomology 2342
- Pseudoconvexity and plurisubharmonic functions 3554
- 𝐿² estimates and existence theorems 5574
- Solutions of the extension and division problems 83102
- Bergman kernels 105124
- Bibliography 115134
- Index 119138
- Back Cover Back Cover1144