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单复变函数 第2卷 英文PDF|Epub|txt|kindle电子书版本下载
- （英）康韦著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：9787510037542
- 出版时间：2011
- 标注页数：396页
- 文件大小：13MB
- 文件页数：410页
- 主题词：单复变函数－英文
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图书目录
13 Return to Basics1
1 Regions and Curves1
2 Derivatives and Other Recollections6
3 Harmonic Conjugates and Primitives14
4 Analytic Arcs and the Reflection Principle16
5 Boundary Values for Bounded Analytic Functions21
14 Conformal Equivalence for Simply Connected Regions29
1 Elementary Properties and Examples29
2 Crosscuts33
3 Prime Ends40
4 Impressions of a Prime End45
5 Boundary Values of Riemann Maps48
6 The Area Theorem56
7 Disk Mappings: The Class S61
15 Conformal Equivalence for Finitely Connected Regions71
1 Analysis on a Finitely Connected Region71
2 Conformal Equivalence with an Analytic Jordan Region76
3 Boundary Values for a Conformal Equivalence Between Finitely Connected Jordan Regions81
4 Convergence of Univalent Functions85
5 Conformal Equivalence with a Circularly Slit Annulus90
6 Conformal Equivalence with a Circularly Slit Disk97
7 Conformal Equivalence with a Circular Region100
16 Analytic Covering Maps109
1 Results for Abstract Covering Spaces109
2 Analytic Covering Spaces113
3 The Modular Function116
4 Applications of the Modular Function123
5 The Existence of the Universal Analytic Covering Map125
17 De Branges's Proof of the Bieberbach Conjecture133
1 Subordination133
2 Loewner Chains136
3 Loewner's Differential Equation142
4 The Milin Conjecture148
5 Some Special Functions156
6 The Proof of de Branges's Theorem160
18 Some Fundamental Concepts from Analysis169
1 Bergman Spaces of Analytic and Harmonic Functions169
2 Partitions of Unity174
3 Convolution in Euclidean Space177
4 Distributions185
5 The Cauchy Tr ansform192
6 An Application: Rational Approximation196
7 Fourier Series and Cesàro Sums198
19 Harmonic Functions Redux205
1 Harmonic Functions on the Disk205
2 Fatou's Theorem210
3 Semicontinuous Functions217
4 Subharmonic Functions220
5 The Logarithmic Potential229
6 An Application: Approximation by Harmonic Functions235
7 The Dirichlet Problem237
8 Harmonic Majorants245
9 The Green Function246
10 Regular Points for the Dirichlet Problem253
11 The Dirichlet Principle and Sobolev Spaces259
20 Hardy Spaces on the Disk269
1 Definitions and Elementa Properties269
2 The Nevanlinna Class272
3 Factorization of Functions in the Nevanlinna Class278
4 The Disk Algebra286
5 The Invariant Subspaces of Hp290
6 Szeg？'s Theorem295
21 Potential Theory in the Plane301
1 Harmonic Measure301
2 The Sweep of a Measure311
3 The Robin Constant313
4 The Green Potential315
5 Polar Sets320
6 More on Regular Points328
7 Logarithmic Capacity: Part 1331
8 Some Applications and Examples of Logarithmic Capacity339
9 Removable Singularities for Functions in the Bergman Space344
10 Logarithmic Capacity:Part 2352
11 The Transfinite Diameter and Logarithmic Capacity355
12 The Refinement of a Subharmonic Function360
13 The Fine Topology367
14 Wiener's criterion for Regular Points376