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Global approximation in harmonic spaces

Authors: Stephen J. Gardiner, Myron Goldstein and Kohur GowriSankaran
Journal: Proc. Amer. Math. Soc. 122 (1994), 213-221
MSC: Primary 41A30; Secondary 31D05
MathSciNet review: 1203986
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Abstract: This paper characterizes, in terms of thinness, compact sets K in a suitable harmonic space $ \Omega $ which have the following property: functions which are harmonic (resp. continuous and superharmonic) on a neighbourhood of K can be uniformly approximated on K by functions which are harmonic (resp. continuous and superharmonic) on $ \Omega $. The corresponding problems of approximating functions which are continuous on K and harmonic (resp. superharmonic) on the interior $ \ring{K}$ are also solved.

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