As well-known, for a given locally compact separable Hausdorff space, a positive Radon measure on with supp = and the space of all continuous functions with compact support on the Beurling and Deny formula states that any regular Dirichlet form on can be expressed as
for all where the symmetric Dirichiet form , the symmetric measure and the measure are uniquely determined by . It is our aim to prove this formula in the non-symmetric case. For this we consider certain families of non-symmetric Dirichlet forms of diffusion type and show that these forms admit an integral representation involving a measure that enjoys some important functional properties as well as in the symmetric case.
Cite this article
S. Mataloni, Representation Formulas for Non-Symmetric Dirichlet Forms. Z. Anal. Anwend. 18 (1999), no. 4, pp. 1039–1064DOI 10.4171/ZAA/927