《多複分析導引》是2007年10月1日人民郵電出版社出版的圖書，作者是(瑞典)霍爾曼德。
基本介紹
- 書名：多複分析導引
- 作者：(瑞典)霍爾曼德
- ISBN：9787115166166
- 頁數：254頁
- 出版社：人民郵電出版社
- 出版時間：第1版 (2007年10月1日)
- 開本：16開
內容簡介,目錄,
內容簡介
這是由世界級數學大師、菲爾茲暨沃爾夫獎得主Hormander撰寫的一部經典的數學著作。作者用統一的觀點處理多復變的基本內容，包括單復變解析函式、多複變函數的基本性質、多複變函數在交換巴拿赫代數中的套用、e運算元的存在性定理和L2方法、Stein流形、解析函式的局部性質以及Stein流形上的凝聚解析層等7章內容，最為精彩的是關於e運算元的L2方法的介紹，其敘述方式至今依然被奉為範本。全書每章都有註記，介紹相關知識點的發展歷史等。
本書可作為高等院校數學系研究生教材和相關研究人員的參考書。
目錄
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
