Analytic Continuation beyond the Ideal Boundary

  • M. Shiba
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 9)


“Analytic continuation beyond the ideal boundary” is a generalization of the corresponding classical notion. The new notion will turn out to be natural and important if we consider not only plane domains but also Riemann surfaces (of finite genus). We survey the new concept in general with a number of examples and study certain simple cases in detail; we give conditions for a function on a noncompact Riemann surface of genus one to be meromorphically continuable beyond the ideal boundary. The classical theorem of Abel plays an important role for our discussion.


Riemann Surface Analytic Continuation Meromorphic Function Conformal Structure Compact Riemann Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • M. Shiba
    • 1
  1. 1.Department of Applied MathematicsHiroshima UniversityHiroshimaJapan

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