報 告 人：宋仁明 教授

報告題目：Approximate factorizations for non-symmetric jump processes

報告時間：2025年6月18日（周三）下午4:00

報告地點：泉山校區5號樓107

主辦單位：數學研究院、數學與統計學院、科學技術研究院

報告人簡介：

   宋仁明，美國Illinois大學教授，1986年河北大學碩士畢業，1989年美國Florida大學博士畢業。訪問過德國、法國、日本、韓國和臺灣等國家和地區的20余所大學和研究所。從事隨機過程和隨機分析研究，在《Trans. Amer. Math. Soc.》、《Proc. London Math. Soc.》、《J. European Math. Soc》、《Math. Ann.》、《J. Funct. Anal.》、《Ann. Probab.》、《Probab. Th. Rel. Fields》、《Stoch. Proc. Appl.》等數學、概率國際權威刊物上發表論文160余篇；多次在國際學術會議上作邀請報告。

報告摘要：

      In this talk, I will talk about a recent paper with Soobin Cho. In this paper, we first extend the approximate factorization for purely discontinuous Markov processes established by Cho-Kim-Song-Vondracek in 2020 by getting rid of some of the conditions. Then we apply the approximate factorization to obtain two-sided heat kernel estimates for three classes of processes: stable-like processes with stable killings in $C^{1, Dini}$ open sets; killed stable-like processes in the setting of the recent preprint  by Kim-Weidner in $C^{1, \epsilon}$ open sets; and non-symmetric stable processes in what we call $C^{1, 2-Dini}$ open sets. In particular, we obtain explicit sharp two-sided heat kernel estimates of killed $\alpha$-stable processes in $C^{1, Dini}$ open sets for all $\alpha\in (0, 2)$ and of censored $\alpha$-stable processes in $C^{1, Dini}$ open sets for $\alpha\in (1, 2)$.