Widder's representation theorem for symmetric local Dirichlet spaces

Details Widder's representation theorem for symmetric local Dirichlet spaces Widder's representation theorem for symmetric local Dirichlet spaces

2012-04-09

arxiv.org/abs/1204.1926v1

Mathematics

Probability

34 pages, submitted to J. Theo. Prob

Scientific paper

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.

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