In the preceding chapters we have discussed regular harmonic and analytic functions. In connection with extremal and mapping problems we have lightly touched on functions with singularities of the form (z — ζ) – n. We have also encountered the singularity — log | z — ζ | which arose in the definition of the Green’s function. It is to this logarithmic singularity that we now direct our attention in more detailed study.


Riemann Surface Logarithmic Singularity Hyperbolic Surface Ideal Boundary Capacity Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1970

Authors and Affiliations

  • L. Sario
    • 1
  • M. Nakai
    • 2
  1. 1.Unversity of CaliforniaCaliforniaUSA
  2. 2.Nagoya UnversityGermany

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