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

   

 

On notions of harmonicity


Author: Zhen-Qing Chen
Journal: Proc. Amer. Math. Soc. 137 (2009), 3497-3510
MSC (2000): Primary 60J45, 31C05; Secondary 31C25, 60J25
Published electronically: May 28, 2009
MathSciNet review: 2515419
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Abstract: In this paper we address the equivalence of the analytic and probabilistic notions of harmonicity in the context of general symmetric Hunt processes on locally compact separable metric spaces. Extensions to general symmetric right processes on Lusin spaces, including infinite dimensional spaces, are mentioned at the end of this paper.


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Additional Information

Zhen-Qing Chen
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: zchen@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09945-6
PII: S 0002-9939(09)09945-6
Keywords: Harmonic function, uniformly integrable martingale, symmetric Hunt process, Dirichlet form, L\'evy system
Received by editor(s): October 25, 2008
Received by editor(s) in revised form: February 16, 2009
Published electronically: May 28, 2009
Additional Notes: The research of this author is supported in part by NSF Grant DMS-0600206.
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2009 Zhen-Qing Chen