Widder's representation theorem for symmetric local Dirichlet spaces
  In classical PDE theory, Widder's theorem gives a representation for nonnegative solutions of the heat equation on $\mathbb{R}^n$. We show that an analogous theorem holds for local weak solutions of the canonical "heat equation" on a symmetric local Dirichlet space satisfying a local parabolic Harnack inequality. 
Nathaniel Eldredge and Laurent Saloff-Coste
math.PR