RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS

RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS

For a compact, nowhere dense set X in the complex plane, C, define Rp(X) as the closure of the rational functions with poles off X in Lp(X, dA). It is well known that for 1 ≤ p < 2, Rp(X) = Lp(X) . Although density may not be achieved for p > 2, there exists a set X so that Rp(X) = Lp(X) for p...

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Bibliographic Details
Main Author: Mattingly, Christopher
Format: Others
Published: UKnowledge 2012
Subjects:
uniform and Lp rational approximation
q > capacity
bounded point evaluations
representing measures
Applied Mathematics
Mathematics
Online Access:http://uknowledge.uky.edu/math_etds/4
http://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1003&amp;context=math_etds
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spelling ndltd-uky.edu-oai-uknowledge.uky.edu-math_etds-10032015-04-11T05:02:38Z RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS Mattingly, Christopher For a compact, nowhere dense set X in the complex plane, C, define Rp(X) as the closure of the rational functions with poles off X in Lp(X, dA). It is well known that for 1 ≤ p < 2, Rp(X) = Lp(X) . Although density may not be achieved for p > 2, there exists a set X so that Rp(X) = Lp(X) for p up to a given number greater than 2 but not after. Additionally, when p > 2 we shall establish that the support of the annihiliating and representing measures for Rp(X) lies almost everywhere on the set of bounded point evaluations of X. 2012-01-01T08:00:00Z text application/pdf http://uknowledge.uky.edu/math_etds/4 http://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1003&amp;context=math_etds Theses and Dissertations--Mathematics UKnowledge uniform and Lp rational approximation q--capacity bounded point evaluations representing measures Applied Mathematics Mathematics
collection NDLTD
format Others
sources NDLTD
topic uniform and Lp rational approximation
q--capacity
bounded point evaluations
representing measures
Applied Mathematics
Mathematics
spellingShingle uniform and Lp rational approximation
q--capacity
bounded point evaluations
representing measures
Applied Mathematics
Mathematics
Mattingly, Christopher
RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS
description For a compact, nowhere dense set X in the complex plane, C, define Rp(X) as the closure of the rational functions with poles off X in Lp(X, dA). It is well known that for 1 ≤ p < 2, Rp(X) = Lp(X) . Although density may not be achieved for p > 2, there exists a set X so that Rp(X) = Lp(X) for p up to a given number greater than 2 but not after. Additionally, when p > 2 we shall establish that the support of the annihiliating and representing measures for Rp(X) lies almost everywhere on the set of bounded point evaluations of X.
author Mattingly, Christopher
author_facet Mattingly, Christopher
author_sort Mattingly, Christopher
title RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS
title_short RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS
title_full RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS
title_fullStr RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS
title_full_unstemmed RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS
title_sort rational approximation on compact nowhere dense sets
publisher UKnowledge
publishDate 2012
url http://uknowledge.uky.edu/math_etds/4
http://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1003&amp;context=math_etds
work_keys_str_mv AT mattinglychristopher rationalapproximationoncompactnowheredensesets
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