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
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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. 
Academic Unit:  Faculty of Science and Engineering > Mathematics and Statistics 
Item ID:  1793 
Identification Number:  https://doi.org/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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