Journal of Theoretical Probability

, Volume 27, Issue 4, pp 1178–1212

Widder’s Representation Theorem for Symmetric Local Dirichlet Spaces


DOI: 10.1007/s10959-013-0484-1

Cite this article as:
Eldredge, N. & Saloff-Coste, L. J Theor Probab (2014) 27: 1178. doi:10.1007/s10959-013-0484-1


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.


Widder’s theoremDirichlet spaceDirichlet form Harnack inequalityParabolic equationNon-negative solution

Mathematics Subject Classification (2010)


Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityNYUSA