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.
Identifer | oai:union.ndltd.org:uky.edu/oai:uknowledge.uky.edu:math_etds-1003 |
Date | 01 January 2012 |
Creators | Mattingly, Christopher |
Publisher | UKnowledge |
Source Sets | University of Kentucky |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Theses and Dissertations--Mathematics |
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