Title page for ETD etd-10132005-152532


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
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 [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.

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