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Banach Spaces, Harmonic Analysis, and Probability Theory pp 103–122Cite as

Qualitative rational approximation on plane compacta

Part of the Lecture Notes in Mathematics book series (LNM,volume 995)

Abstract

Let X be a compact subset of the complex plane. Let R(X) denote the space of all rational functions with poles off X. Let A(X) denote the space of all complex-valued functions on X that are analytic on the interior of X. Let A(X) be a Banach space of functions on X, with R(X)⊂A(X)⊂A(X). Consider the problems: (1) Describe the closure of R(X) in A(X). (2) For which X is R(X) dense in A(X)? There are many results on these problems, for various particular Banach spaces A(X). We offer a point of view from which these results may be viewed systematically.

Keywords

  • Rational Approximation
  • Open Disc
  • Banach Function Space
  • Fine Topology
  • Open 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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Authors
  1. A. G. O’Farrell
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    © 1983 Springer-Verlag

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    O’Farrell, A.G. (1983). Qualitative rational approximation on plane compacta. In: Blei, R.C., Sidney, S.J. (eds) Banach Spaces, Harmonic Analysis, and Probability Theory. Lecture Notes in Mathematics, vol 995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061890

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    • DOI: https://doi.org/10.1007/BFb0061890

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    • Publisher Name: Springer, Berlin, Heidelberg

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