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A Conformal Mapping Technique for Infinitely Connected Regions

Available Formats:
Electronic ISBN: 978-1-4704-0041-5
Product Code: MEMO/1/91.E
List Price: $19.00 MAA Member Price:$17.10
AMS Member Price: $15.20 Click above image for expanded view A Conformal Mapping Technique for Infinitely Connected Regions Available Formats:  Electronic ISBN: 978-1-4704-0041-5 Product Code: MEMO/1/91.E  List Price:$19.00 MAA Member Price: $17.10 AMS Member Price:$15.20
• Book Details

Memoirs of the American Mathematical Society
Volume: 11970; 56 pp
MSC: Primary 30; Secondary 31;
• Table of Contents

• Chapters
• 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 $\mathcal {E}$
• 17. Termination of Green’s lines in ideal boundary points
• 18. The Dirichlet problem in $\mathcal {E}$
• 19. The shaded Dirichlet problem
• 20. Introduction of the hypothesis $m_z(\mathcal {S}) = 0$
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 11970; 56 pp
MSC: Primary 30; Secondary 31;
• Chapters
• 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 $\mathcal {E}$
• 17. Termination of Green’s lines in ideal boundary points
• 18. The Dirichlet problem in $\mathcal {E}$
• 19. The shaded Dirichlet problem
• 20. Introduction of the hypothesis $m_z(\mathcal {S}) = 0$
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.