Widder's representation theorem for symmetric local Dirichlet spaces

Nathaniel Eldredge; Laurent Saloff-Coste

doi:10.1007/s10959-013-0484-1

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arXiv · 1204.1926

Widder's representation theorem for symmetric local Dirichlet spaces

Nathaniel Eldredge·Laurent Saloff-Coste

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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.

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Nathaniel Eldredge, Laurent Saloff-Coste. 2013-02-14. Widder's representation theorem for symmetric local Dirichlet spaces. https://doi.org/10.1007/s10959-013-0484-1

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