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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 Yoshida-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.
Jacob, Niels. "Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.." Revista Matemática Iberoamericana 9.2 (1993): 373-407. <http://eudml.org/doc/39443>.
@article{Jacob1993, abstract = {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 Yoshida-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.}, author = {Jacob, Niels}, journal = {Revista Matemática Iberoamericana}, keywords = {Espacios de Hilbert; Espacios de Sobolev; Procesos de Dirichlet; Principio de máximo de Pontryagin; negative definite functions; Dirichlet forms; symmetric pseudodifferential operators; Feller semigroups; anisotropic Sobolev space; positive maximum principle; probabilistic consequences}, language = {eng}, number = {2}, pages = {373-407}, title = {Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.}, url = {http://eudml.org/doc/39443}, volume = {9}, year = {1993}, }
TY - JOUR AU - Jacob, Niels TI - Further pseudodifferential operators generating Feller semigroups and Dirichlet forms. JO - Revista Matemática Iberoamericana PY - 1993 VL - 9 IS - 2 SP - 373 EP - 407 AB - 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 Yoshida-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. LA - eng KW - Espacios de Hilbert; Espacios de Sobolev; Procesos de Dirichlet; Principio de máximo de Pontryagin; negative definite functions; Dirichlet forms; symmetric pseudodifferential operators; Feller semigroups; anisotropic Sobolev space; positive maximum principle; probabilistic consequences UR - http://eudml.org/doc/39443 ER -