Potential Theory on Compact Sets

<p>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 <em>H</em>(<em>K</em>) on a compact set <em>K</em> in [the set of real numbers]ⁿ. One may let <em>H</em>(<em>K</em>) be the uniform closure of all functions in <em>C</em>(<em>K</em>) which are restrictions of harmonic functions on a neighborhood of <em>K</em>, or take <em>H</em>(<em>K</em>) as the subspace of <em>C</em>(<em>K</em>) consisting of functions which are finely harmonic on the fine interior of <em>K</em>. In [9] it was shown that these definitions are equivalent.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2011

Author dc:creator

• Perkins, Tony

Contributors dc:contributor

• Evgeny A. Poletsky

• Compact sets
• Harmonic functions
• Jensen measures
• Potential Theory
• Restoring Coverings
• Subharmonic functions
• Mathematics

Repository record dc:identifier

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

OAI identifier oai:identifier

oai:surface.syr.edu:mat_etd-1064