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Conformal Mapping Technique for Infinitely Connected Regions.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 1970Copyright date: ©1970Edition: 1st edDescription: 1 online resource (60 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470400415
Subject(s): Genre/Form: Additional physical formats: Print version:: Conformal Mapping Technique for Infinitely Connected RegionsLOC classification:
  • QA360.A77 1970
Online resources:
Contents:
Intro -- 1. INTRODUCTION -- 2. PRELIMINARIES -- I. THE GREEN'S MAPPING -- 3. Green's arcs -- 4. The reduced region and Green's mapping -- 5. Green's lines -- 6. Integrals and arc length in terms of Green's coordinates -- 7. Regular Green's lines -- 8. Green's measure and harmonic measure -- 9. Boundary properties of harmonic and analytic functions -- II. A GENERALIZED POISSON KERNEL AND POISSON INTEGRAL FORMULA -- 10. A generalization of the Poisson kernel -- 11. Properties of the generalized Poisson kernel -- 12. The generalized Poisson integral -- III. AN INVARIANT IDEAL BOUNDARY STRUCTURE -- 13. Construction of the boundary and its topology -- 14. Further properties of the boundary -- 15. Conformal invariance of the ideal boundary structure -- 16. Metrizability, separability, and compactness of ε -- 17. Termination of Green's lines in ideal boundary points -- 18. The Dirichlet problem in ε -- 19. The shaded Dirichlet problem -- 20. Introduction of the hypothesis m[sub(z)](δ) = 0 -- REFERENCES.
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Intro -- 1. INTRODUCTION -- 2. PRELIMINARIES -- I. THE GREEN'S MAPPING -- 3. Green's arcs -- 4. The reduced region and Green's mapping -- 5. Green's lines -- 6. Integrals and arc length in terms of Green's coordinates -- 7. Regular Green's lines -- 8. Green's measure and harmonic measure -- 9. Boundary properties of harmonic and analytic functions -- II. A GENERALIZED POISSON KERNEL AND POISSON INTEGRAL FORMULA -- 10. A generalization of the Poisson kernel -- 11. Properties of the generalized Poisson kernel -- 12. The generalized Poisson integral -- III. AN INVARIANT IDEAL BOUNDARY STRUCTURE -- 13. Construction of the boundary and its topology -- 14. Further properties of the boundary -- 15. Conformal invariance of the ideal boundary structure -- 16. Metrizability, separability, and compactness of ε -- 17. Termination of Green's lines in ideal boundary points -- 18. The Dirichlet problem in ε -- 19. The shaded Dirichlet problem -- 20. Introduction of the hypothesis m[sub(z)](δ) = 0 -- REFERENCES.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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