Qualitative rational approximation on plane compacta.
Banach Spaces, Harmonic Analysis, and Probability Theory Proceedings of the Special Year in Analysis, Held at the University of Connecticut 1980–1981.
Lecture Notes in Mathematics (LNM), 995/1983
Springer Berlin / Heidelberg, pp. 103-122.
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.
||The original publication is available at
||Banach space; function; Plane compacta; Rational approximation.
||Faculty of Science and Engineering > Mathematics and Statistics
Prof. Anthony O'Farrell
||19 Jan 2010 12:00
||Springer Berlin / Heidelberg
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