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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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