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Media type:
E-Article
Title:
Mergelyan pairs for harmonic functions
Contributor:
Gardiner, Stephen
Published:
American Mathematical Society (AMS), 1998
Published in:
Proceedings of the American Mathematical Society, 126 (1998) 9, Seite 2699-2703
Language:
English
DOI:
10.1090/s0002-9939-98-04334-2
ISSN:
1088-6826;
0002-9939
Origination:
Footnote:
Description:
Let Ω ⊆ R n \Omega \subseteq \mathbb R^n be open and E ⊆ Ω E\subseteq \Omega be a bounded set which is closed relative to Ω \Omega . We characterize those pairs ( Ω , E ) (\Omega ,E) such that, for each harmonic function h h on Ω \Omega which is uniformly continuous on E E , there is a sequence of harmonic polynomials which converges to h h uniformly on E E . As an immediate corollary we obtain a characterization of Mergelyan pairs for harmonic functions.