时间：2017年11月23日（周四）9：30-10：30
地点：旗山校区理工楼北601
主办：数学与信息学院
主讲：日本福岡大学 Kazuhiro Kuwae教授
报告摘要：I will talk about an irreducible decomposition for Markov processes associated with quasi-regular symmetric Dirichlet forms or quasi-regular local semi-Dirichlet forms. We do not assume the conservativeness nor the existence of invariant measures for the underlying processes. Moreover, under the absolute continuity condition for transition probability with respect to the underlying measure, we obtain a stronger irreducible decomposition.As an application, we show a compactness of semi-groups under the Green-tightness of underlying measures in the framework of symmetric resolvent strong Feller processes without irreducibility, which improves the recent result on the compactness of semigroups by Takeda. The result is also applied to the proof of $L^p$-independence of spectral radius of for generalized Feynman-Kac semigroupswithout irreducibility. This part is a joint work with Zhen-Qing Chen and Daehong Kim.