Proceedings of the American Mathematical Society

Author(s): Stephen J. Gardiner; Mary Hanley
Journal: Proc. Amer. Math. Soc. 131 (2003), 773-779.
MSC (2000): Primary 31B05; Secondary 41A28
Posted: September 17, 2002
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Abstract: Let

denote a relatively closed subset of the unit ball

of $\mathbb{R} ^{n}$ . The purpose of this paper is to characterize those sets

which have the following property: any harmonic function

which satisfies $\left\vert h\right\vert \leq M$ on

(where

) can be locally uniformly approximated on

by a sequence of harmonic polynomials which satisfy the same inequality on

. This answers a question posed by Stray, who had earlier solved the corresponding problem for holomorphic functions on the unit disc.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 31B05, 41A28

Stephen J. Gardiner
Affiliation: Department of Mathematics, University College Dublin, Dublin 4, Ireland
Email: stephen.gardiner@ucd.ie

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