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# Heat Kernels of Lorentz Cones

Published:1999-06-01
Printed: Jun 1999
• Hongming Ding
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## Abstract

We obtain an explicit formula for heat kernels of Lorentz cones, a family of classical symmetric cones. By this formula, the heat kernel of a Lorentz cone is expressed by a function of time $t$ and two eigenvalues of an element in the cone. We obtain also upper and lower bounds for the heat kernels of Lorentz cones.
 Keywords: Lorentz cone, symmetric cone, Jordan algebra, heat kernel, heat equation, Laplace-Beltrami operator, eigenvalues
 MSC Classifications: 35K05 - Heat equation 43A85 - Analysis on homogeneous spaces 35K15 - Initial value problems for second-order parabolic equations 80A20 - Heat and mass transfer, heat flow

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