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. 103122.
ISBN 9783540123149
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 complexvalued 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/resourcesecured/?target=fulltext.pdf&sid=hxuofv555zqfnbyzcrkpif55&sh=www.springerlink.com 
Keywords: 
Banach space; function; Plane compacta; Rational approximation. 
Subjects: 
Science & Engineering > Mathematics 
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 
URI: 

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