Widder's theorem for Dirichlet spaces

Nate Eldredge (Cornell Univ.)

Abstract: In 1944, Widder proved that a nonnegative solution of the classical heat equation on R^n is uniquely determined by its initial values. I will discuss an extension of this theorem to the context of local Dirichlet spaces, which includes examples such as Riemannian and sub-Riemannian manifolds, complexes, fractals, and other metric measure spaces. This is joint work with Laurent Saloff-Coste.