Continuous functions on polar sets
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- by Ramasamy Jesuraj PDF
- Proc. Amer. Math. Soc. 93 (1985), 262-266 Request permission
Abstract:
Let $\Omega$ be a second countable Brelot harmonic space with a positive potential. If $K$ is a compact subset of $\Omega$ with more than one point, then $K$ is a polar set iff every positive continuous function on $K$ can be extended to a continuous potential on $\Omega = {{\mathbf {R}}^n}(n \geqslant 3)$. This is a generalization of the result proved by H. Wallin for the special case $\Omega = {{\mathbf {R}}^n}(n \geqslant 3)$ with Laplace harmonic space.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 262-266
- MSC: Primary 31D05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770533-9
- MathSciNet review: 770533