SOME REMARKS ON REPRESENTATIONS OF NON-SYMMETRIC LOCAL DIRICHLET FORMS

In this note., we give some remarks on the structure of non-symmetric local Dirichlet forms. We first present LeJan's transformation rule for their co-symmetric parts. Combined with the classical LeJan's Formula, it shows that essentially any local Dirichlet form must be given by differential operators (up to a killing part). Then, is applications, we use this formula to give explicit representations for local Dirichlet forms on both infinite and finite dimensional slate spaces.