Sharp constants in higher-order heat kernel bounds

Nick Dungey

doi:10.1017/s000497270002219x

Sharp constants in higher-order heat kernel bounds

Nick Dungey^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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.

Original language	English
Pages (from-to)	189-200
Number of pages	12
Journal	Bulletin of the Australian Mathematical Society
Volume	61
Issue number	2
DOIs	https://doi.org/10.1017/s000497270002219x
Publication status	Published - Apr 2000

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AB - 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.

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Sharp constants in higher-order heat kernel bounds

Abstract

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