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

Research Report MRR98-053

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

Nick Dungey

Abstract: Let G be a connected Lie group of polynomial growth. We consider m-th order subelliptic differential operators H on G, the semigroups $S_t = e^{-t H}$ and the corresponding heat kernels

. For a large class of H with $m \geq 4$ we demonstrate equivalence between the existence of Gaussian bounds on

, with `good' large t behaviour, and the existence of `cutoff' functions on G. By results of [ERS98], such cutoff functions exist if and only if G is the local direct product of a compact Lie group and a nilpotent Lie group.

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Download paper:	PDF file (207K)
	gzipped DVI file (26K)

Download cover sheet:	PDF file (54K)
	DVI file (2K)