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 Lorentz cone, symmetric cone, Jordan algebra, heat kernel, heat equation, Laplace-Beltrami operator, eigenvalues

MSC Classifications:

35K05, 43A85, 35K15, 80A20 show english descriptions Heat equation
Analysis on homogeneous spaces
Initial value problems for second-order parabolic equations
Heat and mass transfer, heat flow 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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