Journal of Theoretical Probability

, Volume 27, Issue 4, pp 1178–1212 | Cite as

Widder’s Representation Theorem for Symmetric Local Dirichlet Spaces



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 theorem Dirichlet space Dirichlet form  Harnack inequality Parabolic equation Non-negative solution 

Mathematics Subject Classification (2010)

31C25 60J45 35B09 35C15 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityNYUSA

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