A conformal mapping technique for infinitely connected regions /

Methods of classical analysis devised originally for the disc are here extended to more general plane regions by the use of Green's lines, the Green's mapping, and an ideal boundary structure generalizing the prime-end structure of Carathéodory. The regions admitted include all bounded fi...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Arsove, Maynard, 1922-, Johnson, Guy, Jr., 1922-2017 (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence : American Mathematical Society, 1970.
Series:Memoirs of the American Mathematical Society ; no. 91.
Subjects:
Conformal mapping.
Poisson integral formula.
Dirichlet problem.
Boundary value problems.
Mathematical analysis.
Applications conformes.
Problème de Dirichlet.
Problèmes aux limites.
Analyse mathématique.
Poisson integral formula
Mathematical analysis
Dirichlet problem
Boundary value problems
Conformal mapping
Online Access:Texto completo
Table of Contents:
  • Introduction
  • Preliminaries
  • I. The Green's mapping ; Green's arcs
  • The reduced region and Green's mapping
  • Green's lines
  • Integrals and arc length in terms of Green's coordinates
  • Regular Green's lines
  • Green's measure and harmonic measure
  • Boundary properties of harmonic and analytic functions
  • II. A generalized Poisson kernel and Poisson integral formula ; A generalization of the Poisson kernel
  • Properties of the generalized Poisson kernel
  • The generalized Poisson integral
  • III. An invariant ideal boundary structure ; Construction of the boundary and its topology
  • Further properties of the boundary
  • Conformal invariance of the ideal boundary structure
  • Metrizability, separability, and compactness of [script]E
  • Termination of Green's lines in ideal boundary points
  • The Dirichlet problem in [script]E
  • The shaded Dirichlet problem
  • Introduction of the hypothesis [italic]m[italic subscript]z([script]S) = 0.

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