Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Continuous functions on polar sets

Author: Ramasamy Jesuraj
Journal: Proc. Amer. Math. Soc. 93 (1985), 262-266
MSC: Primary 31D05
MathSciNet review: 770533
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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, Notes by K. N. Gowrisankaran and M. K. Venkatesha Murthy. Second edition, revised and enlarged with the help of S. Ramaswamy. Tata Institute of Fundamental Research Lectures on Mathematics, No. 19, Tata Institute of Fundamental Research, Bombay, 1967. MR 0259146 (41 #3788)
  • [2] Corneliu Constantinescu and Aurel Cornea, Potential theory on harmonic spaces, Springer-Verlag, New York-Heidelberg, 1972. With a preface by H. Bauer; Die Grundlehren der mathematischen Wissenschaften, Band 158. MR 0419799 (54 #7817)
  • [3] R.-M. Hervé, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier (Grenoble) 12 (1962), 415–571 (French). MR 0139756 (25 #3186)
  • [4] R. Jesuraj, Continuous functions and exceptional sets in potential theory, Ph.D. Thesis, McGill University, Montreal, 1981.
  • [5] Fumi-Yuki Maeda, Dirichlet integrals on harmonic spaces, Lecture Notes in Mathematics, vol. 803, Springer, Berlin, 1980. MR 576059 (82a:31019)
  • [6] Hans Wallin, Continuous functions and potential theory, Ark. Mat. 5 (1963), 55–84 (1963). MR 0165136 (29 #2425)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 31D05

Retrieve articles in all journals with MSC: 31D05

Additional Information

PII: S 0002-9939(1985)0770533-9
Article copyright: © Copyright 1985 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia