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A Conformal Mapping Technique for Infinitely Connected Regions
Available Formats:
Electronic ISBN: 9781470400415
Product Code: MEMO/1/91.E
List Price: $19.00
MAA Member Price: $17.10
AMS Member Price: $15.20
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A Conformal Mapping Technique for Infinitely Connected Regions
Available Formats:
Electronic ISBN:  9781470400415 
Product Code:  MEMO/1/91.E 
List Price:  $19.00 
MAA Member Price:  $17.10 
AMS Member Price:  $15.20 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 1; 1970; 56 ppMSC: 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 $m_z(\mathcal {S}) = 0$


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 Table of Contents
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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
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