A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approx...A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.展开更多
The uniqueness of the Beurling-Deny first formula in quasi-regular Dirichlet spaces is verified in terms of the strictly strong local property. An extension of the Beurling-Deny second formula is obtained in infinite...The uniqueness of the Beurling-Deny first formula in quasi-regular Dirichlet spaces is verified in terms of the strictly strong local property. An extension of the Beurling-Deny second formula is obtained in infinite dimensional spaces.展开更多
文摘A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.
文摘The uniqueness of the Beurling-Deny first formula in quasi-regular Dirichlet spaces is verified in terms of the strictly strong local property. An extension of the Beurling-Deny second formula is obtained in infinite dimensional spaces.
