On notions of harmonicity

By Zhen-Qing Chen. 2008

55 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a73f4224c21a155d1c9de3e1f3670edffcb179cb

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms (2016, background): “that a function fis said to be locally in FD, denoted as f∈ Floc D , if for every relatively compact subset Uof D, there is a function g∈ FD such that f= gm-a.e. on U. The following is established in [C]. Lemma 2.1. ([C, Lemma 2.6]) Let Dbe an open subset of M. Suppose uis a function in Floc D that ”
Boundary Harnack principle for Δ+Δ^{/2} (2012, background): “on B. The following analytic characterization of a function u being harmonic in D with respect to Xa follows immediately from Example 2.14 in [ 7 ].”
Two‐sided Green function estimates for killed subordinate Brownian motions (2010, methodology): “Using this and the characterization of harmonic functions recently established in [6], we show that Aw ≡ 0 on the half-space (Theorem 4.”
Uniqueness of Brownian motion on Sierpinski carpets (2008, background): “(See [12] for the equivalence of the two notions of harmonicity in a very general framework.”
Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory (2010, unknown): “6 of [7].”