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.
","abstract_html":"<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]<sup>n</sup>. 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>","abstract_has_math":false,"creators":["Perkins, Tony"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Evgeny A. Poletsky"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T04:54:02Z","subjects":["Compact sets","Harmonic functions","Jensen measures","Potential Theory","Restoring Coverings","Subharmonic functions","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://surface.syr.edu/mat_etd/65","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Evgeny A. Poletsky"]},{"key":"dc:creator","label":"Author","values":["Perkins, Tony"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Compact sets","Harmonic functions","Jensen measures","Potential Theory","Restoring Coverings","Subharmonic functions","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://surface.syr.edu/mat_etd/65"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Potential Theory on Compact Sets"]}]}],"canonical_facts":{"dc:contributor":["Evgeny A. Poletsky"],"dc:creator":["Perkins, Tony"],"dc:description.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.
"],"dc:identifier":["https://surface.syr.edu/mat_etd/65"],"dc:subject":["Compact sets","Harmonic functions","Jensen measures","Potential Theory","Restoring Coverings","Subharmonic functions","Mathematics"],"dc:title":["Potential Theory on Compact Sets"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:54:02Z"}