#### 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

#### Recommended Citation

Perkins, Tony, "Potential Theory on Compact Sets" (2011). *Mathematics - Dissertations*. 65.

https://surface.syr.edu/mat_etd/65