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Sharp constants in higher-order heat kernel bounds

Dungey, Nicholas


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 RN. In this case we prove slightly sharper bounds and show that the above-mentioned constant is optimal.

CollectionsANU Research Publications
Date published: 2000
Type: Journal article
Source: Bulletin of the Australian Mathematical Society


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