报告一

报告人：Renming Song

题目：Potential Theory of Subordinate Killed Stable Processes

时间：2017年06月24日 10:00

地点：华中科技大学恩明楼813

摘要：we introduce a large class of subordinators called special subordinators and study their potential theory. Then we study the potential theory of processes obtained by subordinating a killed symmetric stable process in a bounded open setDwith special subordinators. We establish a one-to-one correspondence between the nonnegative harmonic functions of the killed symmetric stable process and the nonnegative harmonic functions of the subordinate killed symmetric stable process. We show that nonnegative harmonic functions of the subordinate killed symmetric stable process are continuous and satisfy a Harnack inequality. We then show that, whenD is a boundedκ-fat set, both the Martin boundary and the minimal Martin boundary of the subordinate killed symmetric stable process inDcoincide with the Euclidean boundary∂D.

报告二

报告人：Renming Song

题目：Potential Theory of Subordinate Killed Stable Processes

时间：2017年06月24日 14:00

地点：华中科技大学恩明楼813

摘要：we introduce a large class of subordinators called special subordinators and study their potential theory. Then we study the potential theory of processes obtained by subordinating a killed symmetric stable process in a bounded open setDwith special subordinators. We establish a one-to-one correspondence between the nonnegative harmonic functions of the killed symmetric stable process and the nonnegative harmonic functions of the subordinate killed symmetric stable process. We show that nonnegative harmonic functions of the subordinate killed symmetric stable process are continuous and satisfy a Harnack inequality. We then show that, whenD is a boundedκ-fat set, both the Martin boundary and the minimal Martin boundary of the subordinate killed symmetric stable process inDcoincide with the Euclidean boundary∂D.