Previous issue ·  Next issue ·  Most recent issue · All issues

# Journal of Operator Theory

Volume 46, Issue 1, Summer 2001  pp. 45-61.

Higher order operators and gaussian bounds on Lie groups of polynomial growth

Authors Nick Dungey
Author institution: Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia

Summary:  Let $G$ be a connected Lie group of polynomial growth. We consider $m$-th order subelliptic differential operators $H$ on $G$, the semigroups $S_t = {\rm e}^{-t H}$ and the corresponding heat kernels $K_t$. For a large class of $H$ with $m \geq 4$ we demonstrate equivalence between the existence of Gaussian bounds on $K_t$, with good" large $t$ behaviour, and the existence of cutoff" functions on $G$. By results of [14], such cutoff functions exist if and only if $G$ is the local direct product of a compact Lie group and a nilpotent Lie group.

Contents    Full-Text PDF