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Approximation on Closed Sets

  • Dieter Gaier

Abstract

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.

Keywords

Compact Subset Entire Function Meromorphic Function Accumulation Point Uniform Approximation 
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

© Birkhäuser Boston, Inc. 1987

Authors and Affiliations

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

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