Conformal Mapping Technique for Infinitely Connected Regions.
Arsove, Maynard G.
Conformal Mapping Technique for Infinitely Connected Regions. - 1st ed. - 1 online resource (60 pages) - Memoirs of the American Mathematical Society ; v.1 . - Memoirs of the American Mathematical Society .
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.
9781470400415
Conformal mapping.
Electronic books.
QA360.A77 1970
Conformal Mapping Technique for Infinitely Connected Regions. - 1st ed. - 1 online resource (60 pages) - Memoirs of the American Mathematical Society ; v.1 . - Memoirs of the American Mathematical Society .
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.
9781470400415
Conformal mapping.
Electronic books.
QA360.A77 1970