Type of Document Dissertation Author Ferry, John URN etd-10132005-152532 Title Rational and harmonic approximation on F.P.A. sets Degree PhD Department Mathematics Advisory Committee

Advisor Name Title Olin, Robert F. Committee Chair McCoy, Robert A. Committee Member Rossi, John F. Committee Member Thomson, James E. Committee Member Wheeler, Robert L. Committee Member Keywords

- Rational equivalence (Algebraic geometry)
Date of Defense 1991-08-15 Availability restricted AbstractLet 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.Files

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