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Mergelyan pairs for harmonic functions


Author: Stephen J. Gardiner
Journal: Proc. Amer. Math. Soc. 126 (1998), 2699-2703
MSC (1991): Primary 31B05; Secondary 41A28
DOI: https://doi.org/10.1090/S0002-9939-98-04334-2
MathSciNet review: 1451804
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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 $h$ 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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Additional Information

Stephen J. Gardiner
Affiliation: Department of Mathematics, University College Dublin, Dublin 4, Ireland
Email: stephen.gardiner@ucd.ie

DOI: https://doi.org/10.1090/S0002-9939-98-04334-2
Received by editor(s): October 21, 1996
Received by editor(s) in revised form: February 3, 1997
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1998 American Mathematical Society

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