Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Mergelyan pairs for harmonic functions

Author: Stephen J. Gardiner
Journal: Proc. Amer. Math. Soc. 126 (1998), 2699-2703
MSC (1991): Primary 31B05; Secondary 41A28
MathSciNet review: 1451804
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 31B05, 41A28

Retrieve articles in all journals with MSC (1991): 31B05, 41A28

Additional Information

Stephen J. Gardiner
Affiliation: Department of Mathematics, University College Dublin, Dublin 4, Ireland
MR Author ID: 71385
ORCID: 0000-0002-4207-8370

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