多元复分析导论 内容简介
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.
多元复分析导论 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
多元复分析导论 节选
《多元复分析导论》内容简介：The idea for this book came when I was an assistant at the Department of Mathe-matics and Computer Science at the Philipps-University Marburg, Germany. Sev-eral times I faced the task of supporting lectures and seminars on complex analysisof 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, letalone 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 sup-porting examples and exercises that helped the student to become familiar withthe fascinating theory of several complex variables.
