Sharp constants in higher-order heat kernel bounds

Research Report MRR99-017

Sharp constants in higher-order heat kernel bounds

Nick Dungey

Abstract: We consider a space X of polynomial type and a self-adjoint operator on L²(X) which is assumed to have a heat kernel satisfying second-order Gaussian bounds. We prove that any power of the operator has a heat kernel satisfying Gaussian bounds with a precise constant in the Gaussian. This constant was previously identified by Barbatis and Davies in the case of powers of the Laplace operator on R^N. In this case we prove slightly sharper bounds and show that the above-mentioned constant is optimal.

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Download paper:	PDF file (197K)
	gzipped DVI file (23K)

Download cover sheet:	PDF file (48K)
	DVI file (1K)