{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/39825"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/39825","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Rational and harmonic approximation on F.P.A. sets","abstract":"Let K be a compact subset of complex N-dimensional space, where N ≥ 1. Let H(K) denote the functions analytic in a neighborhood of K. Let R(K) denote the closure of H(K) in C(K). We study the problem: What is R(K)? The study of R(K) is contained in the field of rational approximation. In a set of lecture notes, T. Gamelin [6] has shown a certain operator to be essential to the study of rational approximation. We study properties of this operator. Now let K be a compact subset of real N-dimensional space, where N ≥ 2. Let harmK denote those functions harmonic in a neighborhood of K. Let h(K) denote the closure of harmK in C(K). We also study the problem: What is h(K)? The study of h(K) is contained in the field of harmonic approximation. As well as obtaining harmonic analogues to our results in rational approximation, we also produce a harmonic analogue to the operator studied in Gamelin's notes.","abstract_html":"Let <i>K</i> be a compact subset of complex <i>N</i>-dimensional space, where <i>N</i> ≥ 1. Let <i>H</i>(<i>K</i>) denote the functions analytic in a neighborhood of <i>K</i>. Let <i>R</i>(<i>K</i>) denote the closure of <i>H</i>(<i>K</i>) in <i>C</i>(<i>K</i>). We study the problem: What is <i>R</i>(<i>K</i>)? The study of <i>R</i>(<i>K</i>) is contained in the field of rational approximation. In a set of lecture notes, T. Gamelin [6] has shown a certain operator to be essential to the study of rational approximation. We study properties of this operator. Now let <i>K</i> be a compact subset of real <i>N</i>-dimensional space, where <i>N</i> ≥ 2. Let harm<i>K</i> denote those functions harmonic in a neighborhood of <i>K</i>. Let <i>h</i>(<i>K</i>) denote the closure of harm<i>K</i> in <i>C</i>(<i>K</i>). We also study the problem: What is <i>h</i>(<i>K</i>)? The study of <i>h</i>(<i>K</i>) is contained in the field of harmonic approximation. As well as obtaining harmonic analogues to our results in rational approximation, we also produce a harmonic analogue to the operator studied in Gamelin's notes.","abstract_has_math":false,"creators":["Ferry, John"],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Olin, Robert F."],"committee_members":["McCoy, Robert A.","Rossi, John F.","Thomson, James E.","Wheeler, Robert L."],"year":1991,"date_issued":"1991-08-15","date_published":"1991-08-15","updated_at":"2026-07-22T22:19:38Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-10132005-152532"],"render_values":[{"text":"etd-10132005-152532","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/39825","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Olin, Robert F."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["McCoy, Robert A.","Rossi, John F.","Thomson, James E.","Wheeler, Robert L."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Ferry, John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:21:01Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:21:01Z","2005-10-13"]},{"key":"dc:date.issued","label":"Date","values":["1991-08-15"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. 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We study the problem: What is R(K)? The study of R(K) is contained in the field of rational approximation. In a set of lecture notes, T. Gamelin [6] has shown a certain operator to be essential to the study of rational approximation. We study properties of this operator. Now let K be a compact subset of real N-dimensional space, where N ≥ 2. Let harmK denote those functions harmonic in a neighborhood of K. Let h(K) denote the closure of harmK in C(K). We also study the problem: What is h(K)? The study of h(K) is contained in the field of harmonic approximation. As well as obtaining harmonic analogues to our results in rational approximation, we also produce a harmonic analogue to the operator studied in Gamelin's notes."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Rational and harmonic approximation on F.P.A. sets"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Olin, Robert F."],"dc:contributor.committeemember":["McCoy, Robert A.","Rossi, John F.","Thomson, James E.","Wheeler, Robert L."],"dc:contributor.department":["Mathematics"],"dc:creator":["Ferry, John"],"dc:date.accessioned":["2014-03-14T21:21:01Z"],"dc:date.available":["2014-03-14T21:21:01Z","2005-10-13"],"dc:date.issued":["1991-08-15"],"dc:description.abstract":["Let K be a compact subset of complex N-dimensional space, where N ≥ 1. Let H(K) denote the functions analytic in a neighborhood of K. Let R(K) denote the closure of H(K) in C(K). We study the problem: What is R(K)? The study of R(K) is contained in the field of rational approximation. In a set of lecture notes, T. Gamelin [6] has shown a certain operator to be essential to the study of rational approximation. We study properties of this operator. Now let K be a compact subset of real N-dimensional space, where N ≥ 2. Let harmK denote those functions harmonic in a neighborhood of K. Let h(K) denote the closure of harmK in C(K). We also study the problem: What is h(K)? The study of h(K) is contained in the field of harmonic approximation. As well as obtaining harmonic analogues to our results in rational approximation, we also produce a harmonic analogue to the operator studied in Gamelin's notes."],"dc:description.degree":["Ph. D."],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-10132005-152532"],"dc:identifier.uri":["http://hdl.handle.net/10919/39825"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Rational and harmonic approximation on F.P.A. sets"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:38Z"}