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Proceedings of the American Mathematical Society

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Continuous functions on polar sets

Author: Ramasamy Jesuraj
Journal: Proc. Amer. Math. Soc. 93 (1985), 262-266
MSC: Primary 31D05
MathSciNet review: 770533
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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 [Enhancements On Off] (What's this?)

  • [1] M. Brelot, Lectures on potential theory, Tata Inst. Fund. Res., Bombay, 1960; reissued 1967. MR 0259146 (41:3788)
  • [2] C. Constantinescu and A. Cornea, Potential theory on harmonic spaces, Springer-Verlag, 1972. MR 0419799 (54:7817)
  • [3] R. M. Herve, Recherches axiomatiques sur la theorie de fonctions surharmoniques et du potential, Ann. Inst. Fourier (Grenoble) 12 (1962), 415-571. MR 0139756 (25:3186)
  • [4] R. Jesuraj, Continuous functions and exceptional sets in potential theory, Ph.D. Thesis, McGill University, Montreal, 1981.
  • [5] F. Y. Maeda, Dirichlet integrals on harmonic spaces, Lecture Notes in Math., vol. 803, Springer-Verlag. MR 576059 (82a:31019)
  • [6] H. Wallin, Continuous functions and potential theory, Ark. Mat. 5 (1963), 55-84. MR 0165136 (29:2425)

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