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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
1970.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 91. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.