Date of Award

2011

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

Evgeny A. Poletsky

Keywords

Compact sets, Harmonic functions, Jensen measures, Potential Theory, Restoring Coverings, Subharmonic functions

Subject Categories

Mathematics

Abstract

The primary goal of this work is to extend the notions of potential theory to compact sets. There are several equivalent ways to define continuous harmonic functions H(K) on a compact set K in [the set of real numbers]n. One may let H(K) be the uniform closure of all functions in C(K) which are restrictions of harmonic functions on a neighborhood of K, or take H(K) as the subspace of C(K) consisting of functions which are finely harmonic on the fine interior of K. In [9] it was shown that these definitions are equivalent.

Access

Open Access

Included in

Mathematics Commons

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