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Media type:
E-Article
Title:
Mergelyan Pairs for Harmonic Functions
Contributor:
Gardiner, Stephen J.
Published:
American Mathematical Society, 1998
Published in:
Proceedings of the American Mathematical Society, 126 (1998) 9, Seite 2699-2703
Language:
English
ISSN:
0002-9939;
1088-6826
Origination:
Footnote:
Description:
<p>Let<tex-math>$\Omega \subseteq {\Bbb R}^{n}$</tex-math>be open and E<tex-math>$\subseteq \Omega $</tex-math>be a bounded set which is closed relative to Ω . We characterize those pairs (Ω , E) such that, for each harmonic function h on Ω 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.</p>