Transactions of the American Mathematical Society

Author(s): Stephen J. Gardiner
Journal: Trans. Amer. Math. Soc. 348 (1996), 251-265.
MSC (1991): Primary 31B05; Secondary 41A30
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 31B05, 41A30

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

DOI: 10.1090/S0002-9947-96-01455-9
PII: S 0002-9947(96)01455-9
Received by editor(s): January 11, 1995
Copyright of article: Copyright 1996, American Mathematical Society

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