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.References
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Additional Information
- Stephen J. Gardiner
- Affiliation: Department of Mathematics, University College Dublin, Dublin 4, Ireland
- MR Author ID: 71385
- ORCID: 0000-0002-4207-8370
- Email: stephen.gardiner@ucd.ie
- Received by editor(s): October 21, 1996
- Received by editor(s) in revised form: February 3, 1997
- Communicated by: Albert Baernstein II
- © Copyright 1998 American Mathematical Society
- 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