TY - JOUR
T1 - Heat Kernel estimates and parabolic harnack inequalities on graphs and resistance forms
AU - Kumagai, Takashi
PY - 2004/9
Y1 - 2004/9
N2 - 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.
AB - 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.
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U2 - 10.2977/prims/1145475493
DO - 10.2977/prims/1145475493
M3 - Article
AN - SCOPUS:9544243679
SN - 0034-5318
VL - 40
SP - 793
EP - 818
JO - Publications of the Research Institute for Mathematical Sciences
JF - Publications of the Research Institute for Mathematical Sciences
IS - 3
ER -