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UNIVERSAL BOUNDS FOR TRACES OF THE DIRICHLET LAPLACE OPERATOR
, 909
"... Abstract. We derive upper bounds for the trace of the heat kernel Z(t) = ..."
Abstract

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Abstract. We derive upper bounds for the trace of the heat kernel Z(t) =
The HardyRellich Inequality for . . .
 PROC. ROY. SOC. EDINBURGH SECT. A
, 1999
"... The HardyRellich inequality given here generalizes a Hardy inequality of Davies [2], from the case of the Dirichlet Laplacian of a region\Omega ` R N to that of the higher order polyharmonic operators with Dirichlet boundary conditions. The inequality yields some immediate spectral information f ..."
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The HardyRellich inequality given here generalizes a Hardy inequality of Davies [2], from the case of the Dirichlet Laplacian of a region\Omega ` R N to that of the higher order polyharmonic operators with Dirichlet boundary conditions. The inequality yields some immediate spectral information for the polyharmonic operators and also bounds on the trace of the associated semigroups and resolvents.
Supported by the Austrian Federal Ministry of Education, Science and Culture
"... Abstract. We derive upper bounds for the trace of the heat kernel Z(t) of the Dirichlet Laplace operator in an open set Ω ⊂ R d, d ≥ 2. In domains of finite volume the result improves an inequality of Kac. Using the same methods we give bounds on Z(t) in domains of infinite volume. For domains of fi ..."
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Abstract. We derive upper bounds for the trace of the heat kernel Z(t) of the Dirichlet Laplace operator in an open set Ω ⊂ R d, d ≥ 2. In domains of finite volume the result improves an inequality of Kac. Using the same methods we give bounds on Z(t) in domains of infinite volume. For domains of finite volume the bound on Z(t) decays exponentially as t tends to infinity and it contains the sharp first term and a correction term reflecting the properties of the short time asymptotics of Z(t). To prove the result we employ refined BerezinLiYau inequalities for eigenvalue means. 1. Introduction and