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Date Available
5-22-2012
Year of Publication
2012
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Mathematics
Faculty
Dr. James E. Brennan
Faculty
Dr. Peter Perry
Abstract
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.
Recommended Citation
Mattingly, Christopher, "RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS" (2012). Theses and Dissertations--Mathematics. 4.
https://uknowledge.uky.edu/math_etds/4
