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6.—Rationally Convex Hulls and Potential Theory.*

Published online by Cambridge University Press:  14 February 2012

Richard F. Basener
Richard F. Basener
Affiliation:
Department of Mathematics, Yale University.
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Synopsis

Let S be a compact subset of the open unit disc in C. Associate to S the set

Let R(X) be the uniform algebra on X generated by the rational functions which are holomorphic near X. It is shown that the spectrum of R(X) is determined in a simple wayby the potential-theoretic properties of S. In particular, the spectrum of R(X) is X if and only if the functions harmonic near S are uniformly dense in the continuous functions on S. Similar results can be obtained for other subsets of C2 constructed from compact subsets of C.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 74 , 1976 , pp. 81 - 89
Copyright
Copyright © Royal Society of Edinburgh 1976

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