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

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发表于2024-11-22

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商品介绍

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

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

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书籍描述

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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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