Mergelyan pairs for harmonic functions

Gardiner, Stephen

doi:10.1090/S0002-9939-98-04334-2

Mergelyan pairs for harmonic functions
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by Stephen J. Gardiner PDF

Proc. Amer. Math. Soc. 126 (1998), 2699-2703 Request permission

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 $h$ on $\Omega$ which is uniformly continuous on $E$, there is a sequence of harmonic polynomials which converges to $h$ uniformly on $E$. As an immediate corollary we obtain a characterization of Mergelyan pairs for harmonic functions.

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