多复变函数是现代数学的一个重要分支，它的研究内容与方法均体现了现代数学间的相互渗透与相互影响。本书是由世界级数学大师撰写的一部经典的数学著作，作者以十分简洁清晰的语言介绍了多复分析的基本内容。

本书是公认的多复分析的标准入门教材，被很多著名大学采用，包括美国的麻省理工学院、加州大学伯克利分校、普度大学等。

这是由世界级数学大师、菲尔兹暨沃尔夫奖得主Hormander撰写的一部经典的数学著作。作者用统一的观点处理多复变的基本内容，包括单复变解析函数、多复变函数的基本性质、多复变函数在交换巴拿赫代数中的应用、e算子的存在性定理和L2方法、Stein流形、解析函数的局部性质以及Stein流形上的凝聚解析层等7章内容，最为精彩的是关于e算子的L2方法的介绍，其叙述方式至今依然被奉为范本。全书每章都有注记，介绍相关知识点的发展历史等。

本书可作为高等院校数学系研究生教材和相关研究人员的参考书。

CHAPTER Ⅰ.ANALYTIC FUNCTIONS OF ONE COMPLEX VARIABLE

Summary

 1.1.Preliminaries

 1.2.Cauchy's integral formula and its applications

 1.3.The Runge approximation theorem

 1.4.The Mittag-Leflter theorcm

 1.5.The Weierstrass theorem

 1.6.Subharmonic functions

Notes

CHAPTER Ⅱ.ELEMENTARY PROPERTIES OF FUNCTIONS OFSEVERAL COMPLEX VARIABLES

Summary

 2.1.Preliminaries

 2.2.Applications of Cauchy's integral formula in polydiscs

 2.3.The inhomogeneous Cauchy—Riemann equations in apolydisc

 2.4.Power series and Reinhardt domains

 2.5.Domains of holomorphy

 2.6.Pseudoconvexity and plurisubharmonicity

 2.7.Runge domains

Notes

CHAPTER Ⅲ.APPLICATIONS TO COMMUTATIVE BANACHALGEBRAS

Summary

 3.1.Preliminaries

 3.2.Analytic functions of elements in a Banach algebra

Notes

CHAPTER Ⅳ.L2 ESTIMATES AND EXISTENCE THEOREMS FOR THE e OPERATOR

Summary

 4.1.Preliminaries

 4.2.Existence theorems in pseudoconvex domains

 4.3.Approximation theorems.

 4.4.Existence theorems in L2 spaces

 4.5.Analytic functionais

Notes

CHAPTER Ⅴ.STEIN MANIFOLDS

Summary

 5.1.Definitions

 5.2.L2 estimates and existence theorems for the e operator

 5.3.Embedding of Stein manifolds

 5.4.Envelopes of holomorphy

 5.5.The Cousin problems on a Stein manifold

 5.6.Existence and approximation theorems for sections of an analytic vector bundle

 5.7.Almost complex manifolds

Notes

CHAPTER Ⅵ.LOCAL PRoPERTIEs OF ANALYTIC FUNCTIONS

Summary

 6.1.The Weierstrass preparation theorem

 6.2.Factorization in the ring A0 of germs of analytic functions

 6.3.Finitely generated A0-modules

 6.4.The Oka theorem

 6.5.Analytic sets

Notes

CHAPTER Ⅶ.COHERENT ANALYTIC SHEAVES ON STEIN MANIFOLDS

Summary

 7.1.Definition of sheaves

 7.2.Existence of global sections of a coherent analytic sheaf

 7.3.Cohomology groups with values in a sheaf.

 7.4.The cohomology groups of a Stein manifold with Coefficients in a coherent analytic sheaf

 7.5.The de Rham theorem

 7.6.Cohomology with bounds and constant coeflicient differential equations

 7.7.Quotients of AK by submodules。and the Ehrenpreis fundamentaI principle

Notes

BIBLIOGRAPHY

INDEX