Approximation on Closed Sets

  • Dieter Gaier


So far, we have approximated functions defined on a compact set K ⊂ ℂ, and the approximating functions were polynomials or rational functions. Now we shall approximate functions defined on a set F that is closed in a domain G. Functions analytic or meromorphic in G will serve as approximating functions. In the special case where G = ℂ, one obtains approximation by entire functions. Here the rate of approximation (as z → ∞) also plays a role. Several of these theorems can be used to construct analytic functions with complicated boundary behavior; we deal with these questions at the end of the chapter, in §5.


Compact Subset Entire Function Meromorphic Function Accumulation Point Uniform Approximation 
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Copyright information

© Birkhäuser Boston, Inc. 1987

Authors and Affiliations

  • Dieter Gaier
    • 1
  1. 1.Mathematisches InstitutJustus-Liebig-UniversitätGiessenWest Germany

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