两类广义Feynman-Kac半群强连续性的探讨

Topics on Strong Continuity of Two Generalized Feynman-Kac Semigroups

研究两类广义Feynman-Kac半群的强连续性问题,这些半群是由一些特定的函数和狄氏过程产生的.得到了广义Feynman-Kac半群强连续,不强连续以及能量测度不在Kato类中的充分条件;构造了一个带跳狄氏型相应的广义Feynman-Kac半群强连续的实例.

In this paper the strongly continuous character of two classes of generalized Feynman-Kac semigroups is stud- ied. These semigroups are produced by some special functions and Dirichlet processes. We obtain the sufficient condition for some particular Feynman-Kac semigroups to be strongly continuous or not. We also obtain the sufficient condition for the energy measures of the functions which produce strongly continuous generalizd Feynman-Kac semigroups to be not in the Kato class. We construct a generalized Feynman-Kac semigroup related with a Dirichlet form with jump that is strongly continuous.