A characterization of harmonic Arakelyan sets

Goldstein, M.; Ow, W. H.

doi:10.1090/S0002-9939-1993-1149971-5

A characterization of harmonic Arakelyan sets
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by M. Goldstein and W. H. Ow PDF

Proc. Amer. Math. Soc. 119 (1993), 811-816 Request permission

Abstract:

Given a closed subset $F$ of either ${R^N},\;N \geqslant 3$, or a Riemann surface, necessary and sufficient conditions are given so that every function continuous on $F$ and harmonic in the interior can be uniformly approximated on $F$ by globally defined harmonic functions.

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