- 单复变函数(第2卷)(英文版)
- - 作者：(英)康韦
  - 出版社：世界图书出版公司
  - ISBN：9787510037542
  - 出版日期：2011/07/01
  - 页数：394
- 售价：19.6

内容大纲
康韦所著的《单复变函数(第2卷)(英文版)》是springer《数学研究生教材》第159卷，系世界著名教学家j。b。coway编写的《单复变函数》之续集，本卷在第1卷的基础上讨论了单复变函数论中的一些专门问题。
作者介绍
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
  1 analysis on a finitely connected region.
  2 conformal equivalence with an analytic jordan region
  3 boundary values for a conformed equivalence between finitelyconnected jordan regions
  4 convergence of univalent functions
  5 conformed 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 szegs'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

内容大纲

作者介绍

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