1. CMB 1999 (vol 42 pp. 169)
|Heat Kernels of Lorentz Cones |
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
Categories:35K05, 43A85, 35K15, 80A20