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A Conformal Mapping Technique for Infinitely Connected Regions
 
Front Cover for 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
Front Cover for A Conformal Mapping Technique for Infinitely Connected Regions
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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
  • 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.