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Representation of continuous functions
as sums of Green functions

Author: Stephen J. Gardiner
Journal: Proc. Amer. Math. Soc. 124 (1996), 1149-1157
MSC (1991): Primary 31B05
MathSciNet review: 1307519
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Abstract: Let $K\subset \Omega\subseteq \mathbb{R}^n$, where $K$ is polar and compact and $\Omega$ is a domain with Green function $G_\Omega({\boldsymbol\cdot},{\boldsymbol\cdot} )$. We characterize those subsets $E$ of $\Omega\backslash K$ which have the following property: Every positive continuous function on $K$ can be written as $\sum_k\lambda_kG_\Omega(x_k, {\boldsymbol\cdot})$, where $x_k\in E$ and $\lambda_k>0$ for each $k$.

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Additional Information

Stephen J. Gardiner
Affiliation: Department of Mathematics, University College, Dublin 4, Ireland

Received by editor(s): June 14, 1994
Received by editor(s) in revised form: October 4, 1994
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society