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Sharp constants in higher-order heat kernel bounds

Published online by Cambridge University Press:  17 April 2009

Nick Dungey
Nick Dungey
Affiliation:
Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia e-mail: dungey@maths.anu.edu.au Australia
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 189 - 200
Copyright
Copyright © Australian Mathematical Society 2000

References

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