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Fall 2008 A characterization of $C(K)$ among function algebras on a Riemann surface
Lynette J. Boos
Illinois J. Math. 52(3): 867-885 (Fall 2008). DOI: 10.1215/ijm/1254403719

Abstract

For a compact subset $K$ of a Riemann surface, necessary and sufficient conditions are given for a function algebra containing $A(K)$ to be all of $C(K)$. Using these results, several conditions are given on a complex-valued function $f$ so that the algebra generated by $A(K)$ and $f$ is all of $C(K)$. In particular, the results are applied to a harmonic function $f$ to give sufficient conditions for the algebra generated by $A(K)$ and $f$ to be all of $C(K)$. Also, sufficient conditions are given for the algebra $A(K)$ to be a maximal subalgebra of $C(K)$.

Citation

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Lynette J. Boos. "A characterization of $C(K)$ among function algebras on a Riemann surface." Illinois J. Math. 52 (3) 867 - 885, Fall 2008. https://doi.org/10.1215/ijm/1254403719

Information

Published: Fall 2008
First available in Project Euclid: 1 October 2009

zbMATH: 1192.46048
MathSciNet: MR2546012
Digital Object Identifier: 10.1215/ijm/1254403719

Subjects:
Primary: 32A38 , 46J10
Secondary: 30F15

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

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Vol.52 • No. 3 • Fall 2008
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