Arsove, Maynard G.
A conformal mapping technique for infinitely connected regions / [electronic resource] by Maynard G. Arsove and Guy Johnson, Jr. - Providence, R.I. : American Mathematical Society, c1970. - 1 online resource (56 p. : ill.) - Memoirs of the American Mathematical Society, v. 91 0065-9266 (print); 1947-6221 (online); . - Memoirs of the American Mathematical Society ; no. 91. .
Includes bibliographical references.
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 $\mathcal $ 17. Termination of Green's lines in ideal boundary points 18. The Dirichlet problem in $\mathcal $ 19. The shaded Dirichlet problem 20. Introduction of the hypothesis $m_z(\mathcal ) = 0$
Access is restricted to licensed institutions
Electronic reproduction.
Providence, Rhode Island :
American Mathematical Society.
2012
Mode of access : World Wide Web
9781470400415 (online)
Conformal mapping.
QA3 / .A57 no. 91
A conformal mapping technique for infinitely connected regions / [electronic resource] by Maynard G. Arsove and Guy Johnson, Jr. - Providence, R.I. : American Mathematical Society, c1970. - 1 online resource (56 p. : ill.) - Memoirs of the American Mathematical Society, v. 91 0065-9266 (print); 1947-6221 (online); . - Memoirs of the American Mathematical Society ; no. 91. .
Includes bibliographical references.
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 $\mathcal $ 17. Termination of Green's lines in ideal boundary points 18. The Dirichlet problem in $\mathcal $ 19. The shaded Dirichlet problem 20. Introduction of the hypothesis $m_z(\mathcal ) = 0$
Access is restricted to licensed institutions
Electronic reproduction.
Providence, Rhode Island :
American Mathematical Society.
2012
Mode of access : World Wide Web
9781470400415 (online)
Conformal mapping.
QA3 / .A57 no. 91