THE HEAT EQUATION ON A MATRIX SPACE

摘要

On the space of real matrices, an analog of the heat equation is studied. On the basis of properties of a heat source, the solution of the Cauchy problem with an initial radiation defined at the vertex of the cone of positive definite symmetric matrices is constructed. A relation between the Riesz potentials associated with composite power functions on a matrix space and the solutions of the heat equation is established.