THE DAVIES METHOD FOR HEAT KERNEL UPPER BOUNDS OF NON-LOCAL DIRICHLET FORMS ON ULTRA-METRIC SPACES

doi:10.1007/s10473-020-0506-x

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (5): 1240-1248.doi: 10.1007/s10473-020-0506-x

THE DAVIES METHOD FOR HEAT KERNEL UPPER BOUNDS OF NON-LOCAL DIRICHLET FORMS ON ULTRA-METRIC SPACES

高晋

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2019-03-12 修回日期:2019-09-14 出版日期:2020-10-25 发布日期:2020-11-04
作者简介:Jin GAO,E-mail:gao-j17@mails.tsinghua.edu.cn
基金资助:
The author was supported by National Natural Science Foundation of China (11871296).

THE DAVIES METHOD FOR HEAT KERNEL UPPER BOUNDS OF NON-LOCAL DIRICHLET FORMS ON ULTRA-METRIC SPACES

Jin GAO

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2019-03-12 Revised:2019-09-14 Online:2020-10-25 Published:2020-11-04
Supported by:
The author was supported by National Natural Science Foundation of China (11871296).

摘要/Abstract

摘要： We apply the Davies method to give a quick proof for the 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 a radius larger than the truncated range. This new phenomenon arises from the ultra-metric property of the space.

关键词: heat kernel, ultra-metric, Davies method

Abstract: We apply the Davies method to give a quick proof for the 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 a radius larger than the truncated range. This new phenomenon arises from the ultra-metric property of the space.

Key words: heat kernel, ultra-metric, Davies method

中图分类号:

35K08

高晋. THE DAVIES METHOD FOR HEAT KERNEL UPPER BOUNDS OF NON-LOCAL DIRICHLET FORMS ON ULTRA-METRIC SPACES[J]. 数学物理学报(英文版), 2020, 40(5): 1240-1248.

Jin GAO. THE DAVIES METHOD FOR HEAT KERNEL UPPER BOUNDS OF NON-LOCAL DIRICHLET FORMS ON ULTRA-METRIC SPACES[J]. Acta mathematica scientia,Series B, 2020, 40(5): 1240-1248.

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THE DAVIES METHOD FOR HEAT KERNEL UPPER BOUNDS OF NON-LOCAL DIRICHLET FORMS ON ULTRA-METRIC SPACES

THE DAVIES METHOD FOR HEAT KERNEL UPPER BOUNDS OF NON-LOCAL DIRICHLET FORMS ON ULTRA-METRIC SPACES

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