Qualitative rational approximation on plane compacta.

O'Farrell, A.G. (1983) Qualitative rational approximation on plane compacta. In: 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. ISBN 978-3-540-12314-9

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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.

Item Type: Book Section
Additional Information: The original publication is available at https://commerce.metapress.com/content/2v1077857400g443/resource-secured/?target=fulltext.pdf&sid=hxuofv555zqfnbyzcrkpif55&sh=www.springerlink.com
Keywords: Banach space; function; Plane compacta; Rational approximation.
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1793
Identification Number: 10.1007/BFb0061883
Depositing User: Prof. Anthony O'Farrell
Date Deposited: 19 Jan 2010 12:00
Publisher: Springer Berlin / Heidelberg
Refereed: Yes

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