多变量复分析导论
多变量复分析导论封面图

多变量复分析导论

(德) 谢德曼 (Scheidemann,V.) , 著

出版社:世界图书出版公司北京公司

年代:2010

定价:35.0

书籍简介:

本书全面介绍了多变量复分析,旨在全面清晰地介绍多变复分析,而非包揽尽可能多的相关材料。书中包括了不少相关的数学概念,如泛函分析和代数,以丰富书的内容。书中还集中讲述了一维的情况,例如著名的Hartog的Kugelsatz,Carton-Thullen定理和Bochner定理。

书籍目录:

preface

1 elementary theory of several complex variables

1.1 geometry of cn

1.2 holomorphic functions in several complex variables

1.2.1 definition of a holomorphic function

1.2.2 basic properties of holomorphic functions

1.2.3 partially holomorphic functions and the cauchy-pdemann differential equations

1.3 the cauchy integral formula

1.4 o (u) as a topological space

1.4.1 locally convex spaces

1.4.2 the compact-open topology on c (u, e)

1.4.3 the theorems of arzela-ascoli and montel

1.5 power series and taylor series

1.5.1 summable families in banach spaces

1.5.2 power series

1.5.3 reinhardt domains and laurent expansion

2 continuation on circular and polycircular domains

2.1 holomorphic continuation

2.2 representation-theoretic interpretation of the laurent series

2.3 hartogs' kugelsatz, special case

3 biholomorphic maps

3.1 the inverse function theorem and implicit functions

3.2 the riemann mapping problem

3.3 cartan's uniqueness theorem

4 analytic sets

4.1 elementary properties of analytic sets

4.2 the riemann removable singularity theorems

5 hartogs' kugelsatz

5.1 holomorphic differential forms

5.1.1 multilinear forms

5.1.2 complex differential forms

5.2 the inhomogenous cauchy-riemann differential equations

5.3 dolbeaut's lemma

5.4 the kugelsatz of hartogs

6 continuation on tubular domains

6.1 convex hulls

6.2 holomorphically convex hulls

6.3 bochner's theorem

7 cartan-thullen theory

7.1 holomorphically convex sets

7.2 domains of holomorphy

7.3 the theorem of cartan-thullen

7.4 holomorphically convex reinhardt domains

8 local properties of holomorphic functions

8.1 local representation of a holomorphic function

8.1.1 germ of a holomorphic function

8.1.2 the algebras of formal and of convergent power series

8.2 the weierstrass theorems

8.2.1 the weierstrass division formula

8.2.2 the weierstrass preparation theorem

8.3 algebraic properties of c {z1,., z

内容摘要:

The idea for this book came when I was an assistant at the Department of Mathematics and Computer Science at the Philipps-University Marburg, Germany. Several times I faced the task of supporting lectures and seminars on complex analysis of several variables and found out that there are very few books on the subject,compared to the vast amount of literature on function theory of one variable, let alone on real variables or basic algebra. Even fewer books, to my understanding,were written primarily with the student in mind. So it was quite hard to find supporting examples and exercises that helped the student to become familiar with the fascinating theory of several complex variables.

书籍规格:

书籍详细信息
书名多变量复分析导论站内查询相似图书
9787510027277
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出版地北京出版单位世界图书出版公司北京公司
版次影印本印次1
定价(元)35.0语种英文
尺寸26 × 19装帧平装
页数 184 印数 1000

书籍信息归属:

多变量复分析导论是世界图书出版公司北京公司于2010.9出版的中图分类号为 O174.5 的主题关于 多变量-复分析-英文 的书籍。