Some Conditions for Decay of Convolution Powers and Heat Kernels on Groups

[摘要] Let $K$ be a function on a unimodular locally compact group$G$, and denote by $K_n = K*K* cdots * K$ the $n$-th convolutionpower of $K$.Assuming that $K$ satisfies certain operator estimates in $L^2(G)$,we give estimates ofthe norms $|K_n|_2$ and $|K_n|_infty$for large $n$.In contrast to previous methods for estimating $|K_n|_infty$,we do not need to assume thatthe function $K$ is a probability density or non-negative.Our results also adapt for continuous time semigroups on $G$.Various applications are given, for example, to estimates ofthe behaviour of heat kernels on Lie groups.

[学科分类] 数学（综合）