Widder’s Representation Theorem for Symmetric Local Dirichlet Spaces

Nathaniel Eldredge () and Laurent Saloff-Coste ()
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Nathaniel Eldredge: Cornell University
Laurent Saloff-Coste: Cornell University

Journal of Theoretical Probability, 2014, vol. 27, issue 4, 1178-1212

Abstract: Abstract In classical PDE theory, Widder’s theorem gives a representation for non-negative 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.

Keywords: Widder’s theorem; Dirichlet space; Dirichlet form; Harnack inequality; Parabolic equation; Non-negative solution; 31C25; 60J45; 35B09; 35C15 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-013-0484-1

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