On notions of harmonicity

2008/10/28 by Chen, Zhen-Qing · 4 citations
#31C05 (Primary) #31C25 #60J25 (Secondary) #60J45 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0810.5089

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.

Cited by

• Abnormal boundary decay for stable operators
• Isolated Singularities and Measure Data Problems for Semilinear Equations Driven by Stable Lévy Operators
• Nonlinear Hardy-Stein type identities for harmonic functions relative to symmetric integro-differential operators
• A remark on subharmonicity for symmetric Dirichlet forms

Related

• On subhamonicity for symmetric Markov processes
• Faber-Krahn type inequalities and uniqueness of positive solutions on\n metric measure spaces
• On the harmonic measure of stable processes
• Liouville property, Wiener's test and unavoidable sets for Hunt\n processes
• Symmetric jump processes: localization, heat kernels, and convergence