Let （X<sub>l</sub>） be an m-symmetric Hunt process associated with a regular Dirichlet form on L<sup>2</sup>（X; m）. S<sub>0</sub> denotes the family of all Radon measures of fin...Let （X<sub>l</sub>） be an m-symmetric Hunt process associated with a regular Dirichlet form on L<sup>2</sup>（X; m）. S<sub>0</sub> denotes the family of all Radon measures of finite energy integral. It is shown that μ∈S<sub>0</sub> iff α】0 such that μRα【【m and d（μR<sub>α</sub>）/dm∈. We have U<sub>α</sub>μ=d（μR<sub>α</sub>）/dm if μ∈S<sub>0</sub>. As an application, we obtain some criteria for conservativeness of （X<sub>l</sub>）.展开更多
We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover. we apply t...We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover. we apply this quasi-homeomorphism method to study the measures of finite energy integrals of generalized Dirichlet forms. We show that any 1-coexcessive function which is dominated by a function in is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is-exceptional if and only if μ(B)=0 for any measure μ of finite energy integral.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Let （X<sub>l</sub>） be an m-symmetric Hunt process associated with a regular Dirichlet form on L<sup>2</sup>（X; m）. S<sub>0</sub> denotes the family of all Radon measures of finite energy integral. It is shown that μ∈S<sub>0</sub> iff α】0 such that μRα【【m and d（μR<sub>α</sub>）/dm∈. We have U<sub>α</sub>μ=d（μR<sub>α</sub>）/dm if μ∈S<sub>0</sub>. As an application, we obtain some criteria for conservativeness of （X<sub>l</sub>）.
文摘We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover. we apply this quasi-homeomorphism method to study the measures of finite energy integrals of generalized Dirichlet forms. We show that any 1-coexcessive function which is dominated by a function in is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is-exceptional if and only if μ(B)=0 for any measure μ of finite energy integral.
