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.
|ジャーナル||Publications of the Research Institute for Mathematical Sciences|
|出版ステータス||Published - 2004 9月|
ASJC Scopus subject areas
- 数学 (全般)