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Davies method for heat kernel upper bounds of non-local Dirichlet forms on ultra-metric spaces (1912.11190v1)
Published 24 Dec 2019 in math.FA, math.AP, and math.PR
Abstract: We apply the Davies method to give a quick proof for upper estimate of the heat kernel for the non-local Dirichlet form on the ultra-metric space. The key observation is that the heat kernel of the truncated Dirichlet form vanishes when two spatial points are separated by any ball of radius larger than the truncated range. This new phenomenon arises from the ultra-metric property of the space.
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