We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yosida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.
Cite this article
Niels Jacob, Further pseudodifferential operators generating Feller semigroups and Dirichlet forms. Rev. Mat. Iberoam. 9 (1993), no. 2, pp. 373–407