Heat Kernel estimates and parabolic harnack inequalities on graphs and resistance forms

Takashi Kumagai*

*この研究の対応する著者

研究成果: Article査読

29 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)793-818
ページ数26
ジャーナルPublications of the Research Institute for Mathematical Sciences
40
3
DOI
出版ステータスPublished - 2004 9月
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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