RATIONAL APPROXIMATION ON COMPACT NOWHERE DENSE SETS

Author

Christopher Mattingly, University of KentuckyFollow

Date Available

5-22-2012

Year of Publication

2012

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department/School/Program

Mathematics

First Advisor

Dr. James E. Brennan

Abstract

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