Widder's representation theorem for symmetric local Dirichlet spaces

Abstract

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.

33 pages, to appear in Journal of Theoretical Probability. This version incorporates all revisions made during the peer review process and is intended to be equivalent to the published version (though formatting, theorem numbering, etc, will differ)

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