Date of Award
Doctor of Philosophy (PhD)
Evgeny A. Poletsky
Compact sets, Harmonic functions, Jensen measures, Potential Theory, Restoring Coverings, Subharmonic functions
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  it was shown that these definitions are equivalent.
Perkins, Tony, "Potential Theory on Compact Sets" (2011). Mathematics - Dissertations. Paper 65.