Proceedings of the American Mathematical Society

Author(s): Stephen J. Gardiner
Journal: Proc. Amer. Math. Soc. 126 (1998), 2699-2703.
MSC (1991): Primary 31B05; Secondary 41A28
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Abstract: Let $\Omega\subseteq\mathbb R^n$ be open and $E\subseteq \Omega$ be a bounded set which is closed relative to $\Omega$ . We characterize those pairs $(\Omega,E)$ such that, for each harmonic function

on $\Omega$ which is uniformly continuous on

, there is a sequence of harmonic polynomials which converges to

uniformly on

. As an immediate corollary we obtain a characterization of Mergelyan pairs for harmonic functions.

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