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Uniform harmonic approximation of bounded functions

Authors:	Stephen J Gardiner

Institution:	Department of Mathematics, University College Dublin, Dublin 4, Ireland

Abstract:	Let $\Omega$ be an open set in $\mathbb R^n$ and be a relatively closed subset of $\Omega$ . We characterize those pairs $(\Omega,E)$ which have the following property: every function which is bounded and continuous on and harmonic on can be uniformly approximated by functions harmonic on $\Omega$ . Several related results concerning both harmonic and superharmonic approximation are also established.

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