单复变函数(第2卷) [Functions of One Complex Variable 2]

单复变函数(第2卷) [Functions of One Complex Variable 2] 下载 mobi epub pdf 电子书 2024


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发表于2024-11-25

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出版社: 世界图书出版公司
ISBN:9787510037542
版次:1
商品编码:10914302
包装:平装
外文名称:Functions of One Complex Variable 2
开本:24开
出版时间:2011-07-01
页数:394
正文语种:英文


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内容简介

This is the sequel to my book Functions of One Complex Variable I, and probably a good opportunity to express my appreciation to the mathemat-ical community for its reception of that work. In retrospect, writing that book was a crazy venture.As a graduate student I had had one of the worst learning experiences of my career when I took complex analysis; a truly bad teacher. As a non-tenured assistant professor, the department allowed me to teach the graduate course in complex analysis. They thought I knew the material; I wanted to learn it. I adopted a standard text and shortly after beginning to prepare my lectures I became dissatisfied. All the books in print had virtues; but I was educated as a modern analyst, not a classical one, and they failed to satisfy me.

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目录

Preface
13 Return to Basics
1 Regions and Curves
2 Derivatives and Other Recollections
3 Harmonic Conjugates and Primitives
4 Analytic Arcs and the Reflection Principle
5 Boundary Values for Bounded Analytic Functions

14 Conformal Equivalence for Simply Connected Regions
1 Elementary Properties and Examples
2 Crosscuts
3 Prime Ends
4 Impressions of a Prime End
5 Boundary Values of Riemann Maps
6 The Area Theorem
7 Disk Mappings: The Class

15 Conformal Equivalence for Finitely Connected Regions
I Analysis on a Finitely Connected Region
2 Conformal Equivalence with an Analytic Jordan Region
3 Boundary Values for a Conformal Equivalence Between Finitely Connected Jordan Regions
4 Convergence of Univalent Functions
5 Conformal Equivalence with a Circularly Slit Annulus
6 Conformal Equivalence with a Circularly Slit Disk
7 Conformal Equivalence with a Circular Region

16 Analytic Covering Maps
1 Results for Abstract Covering Spaces
2 Analytic Covering Spaces
3 The Modular Function
4 Applications of the Modular Function
5 The Existence of the Universal Analytic Covering Map

17 De Branges's Proof of the Bieberbach Conjecture
1 Subordination
2 Loewner Chains
3 Loewner's Differential Equation
4 The Milin Conjecture
5 Some Special Functions
6 The Proof of de Branges's Theorem

18 Some Fundamental Concepts from Analysis
1 Bergman Spaces of Analytic and Harmonic Functions
2 Partitions of Unity
3 Convolution in Euclidean Space
4 Distributions
5 The Cauchy Transform
6 An Application: Rational Approximation
7 Fourier Series and Cesaro Sums

19 Harmonic Functions Redux
1 Harmonic Functions on the Disk
2 Fatou's Theorem
3 Semicontinuous Functions
4 Subharmonic Functions
5 The Logarithmic Potential
6 An Application: Approximation by Harmonic Functions
7 The Dirichlet Problem
8 Harmonic Majorants
9 The Green Function
10 Regular Points for the Dirichlet Problem
11 The Dirichlet Principle and Sobolev Spaces

20 Hardy Spaces on the Disk
1 Definitions and Elementary Properties
2 The Nevanlinna Class
3 Factorization of Functions in the Nevanlinna Class
4 The Disk Algebra
5 The Invariant Subspaces of Hp
6 Szego's Theorem

21 Potential Theory in the Plane
1 Harmonic Measure
2 The Sweep of a Measure
3 The Robin Constant
4 The Green Potential
5 Polar Sets
6 More on Regular Points
7 Logarithmic Capacity: Part 1
8 Some Applications and Examples of Logarithmic Capacity
9 Removable Singularities for Functions in the Bergman Space
10 Logarithmic Capacity: Part 2
11 The Transfinite Diameter and Logarithmic Capacity
12 The Refinement of a Subharmonic Function
13 The Fine Topology
14 Wiener's criterion for Regular Points
Contents
References
List of Symbols
Index

前言/序言



单复变函数(第2卷) [Functions of One Complex Variable 2] 下载 mobi epub pdf txt 电子书 格式

单复变函数(第2卷) [Functions of One Complex Variable 2] mobi 下载 pdf 下载 pub 下载 txt 电子书 下载 2024

单复变函数(第2卷) [Functions of One Complex Variable 2] 下载 mobi pdf epub txt 电子书 格式 2024

单复变函数(第2卷) [Functions of One Complex Variable 2] 下载 mobi epub pdf 电子书
想要找书就要到 图书大百科
立刻按 ctrl+D收藏本页
你会得到大惊喜!!

用户评价

评分

This is the sequel to Functions of One Complex Variable I。All the books in print had virtues

评分

不错,内容好,质量也好。

评分

书是好书,不过书角都给摔坏了。。

评分

非常非常好

评分

不错,内容好,质量也好。

评分

书一般般吧。帮朋友买的。

评分

非常好的书,很开心买到最后一本。

评分

非常非常好

评分

既然这书我买了上册,下册不买的话,我怎么读的通啊。开玩笑的,基本当当参考资料了

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单复变函数(第2卷) [Functions of One Complex Variable 2] mobi epub pdf txt 电子书 格式下载 2024


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