Heat Kernel Estimates and Parabolic Harnack Inequalities on Graphs and Resistance Forms
Heat Kernel Estimates and Parabolic Harnack Inequalities on Graphs and Resistance Forms
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DOI：
10.2977/prims/1145475493
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发表时间：
2004-09
影响因子：
1.2
通讯作者：
T. Kumagai
中科院分区：
文献类型：
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作者：
T. Kumagai
本文综述了图的热核估计和抛物型Harnack不等式的最新研究成果，其中时间尺度是空间尺度的β次方，且β ≥ 2.然后，我们讨论了自伴算子诱导的阻力形式。利用阻力度量，我们给出了详细的热核估计和抛物Harnack不等式的一个简单的条件。作为一个应用，我们表明，在树木的详细的双边热核估计是等价于一些体积增长条件。
We summarize recent work on heat kernel estimates and parabolic Harnack inequalities for graphs, where the time scale is the β-th power of the space scale for some β ≥ 2. We then discuss self-adjoint operators induced by resistance forms. Using a resistance metric, we give a simple condition for detailed heat kernel estimates and parabolic Harnack inequalities. As an application, we show that on trees a detailed two-sided heat kernel estimate is equivalent to some volume growth condition.