Rational and harmonic approximation on F.P.A. sets

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dc.contributor.authorFerry, Johnen
dc.contributor.committeechairOlin, Robert F.en
dc.contributor.committeememberMcCoy, Robert A.en
dc.contributor.committeememberRossi, John F.en
dc.contributor.committeememberThomson, James E.en
dc.contributor.committeememberWheeler, Robert L.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:21:01Zen
dc.date.adate2005-10-13en
dc.date.available2014-03-14T21:21:01Zen
dc.date.issued1991-08-15en
dc.date.rdate2005-10-13en
dc.date.sdate2005-10-13en
dc.description.abstractLet <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.en
dc.description.degreePh. D.en
dc.format.extentvi, 164en
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-10132005-152532en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10132005-152532/en
dc.identifier.urihttp://hdl.handle.net/10919/39825en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1991.F477.pdfen
dc.relation.isformatofOCLC# 24707058en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1991.F477en
dc.subject.lcshRational equivalence (Algebraic geometry)en
dc.titleRational and harmonic approximation on F.P.A. setsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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