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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Uniform harmonic approximation
of bounded functions


Author: Stephen J. Gardiner
Journal: Trans. Amer. Math. Soc. 348 (1996), 251-265
MSC (1991): Primary 31B05; Secondary 41A30
DOI: https://doi.org/10.1090/S0002-9947-96-01455-9
MathSciNet review: 1316850
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Abstract: Let $\Omega$ be an open set in $\mathbb R^n$ and $E$ 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 $E$ and harmonic on $E^0$ 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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Additional Information

Stephen J. Gardiner
Affiliation: Department of Mathematics, University College Dublin, Dublin 4, Ireland

DOI: https://doi.org/10.1090/S0002-9947-96-01455-9
Received by editor(s): January 11, 1995
Article copyright: © Copyright 1996 American Mathematical Society