Runge Theory for Regions

  • Reinhold Remmert
Part of the Graduate Texts in Mathematics book series (GTM, volume 172)


In Chapter 12 we proved approximation theorems for compact sets; we now prove their analogues for regions. We pose the following question:

When are regions D, D’ with D ⊂ D’ a Runge pair? That is, when can every function holomorphic in D be approximated compactly by functions holomorphis in D’?


Compact Space Approximation Theorem Unbounded Component Compact Component Polynomially Convex 
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 New York 1998

Authors and Affiliations

  • Reinhold Remmert
    • 1
  1. 1.Mathematisches InstitutWestfälische Wilhelms—Universität MünsterMünsterGermany

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