Rational and harmonic approximation on F.P.A. sets
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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.
- Doctoral Dissertations