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dc.contributor.authorFerry, Johnen_US

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 [6J 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.publisherVirginia Techen_US
dc.subjectRational equivalence (Algebraic geometry)en_US
dc.subject.lccLD5655.V856 1991.F477en_US
dc.titleRational and harmonic approximation on F.P.A. setsen_US
dc.description.degreePh. D.en_US D.en_US Polytechnic Institute and State Universityen_US
dc.contributor.committeechairOlin, Robert F.en_US
dc.contributor.committeememberMcCoy, Robert A.en_US
dc.contributor.committeememberRossi, John F.en_US
dc.contributor.committeememberThomson, James E.en_US
dc.contributor.committeememberWheeler, Robert L.en_US

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