报告题目：The eigenvalue counting problem of a class of Sturm-Liouville problems and its applications

报 告 人：陈潇（山东大学（威海））

报告时间：2023年3月6日 14:30-15:30

报告地点：腾讯会议 569680716

主办单位：威廉希尔中文网站

报告摘要：In this talk, we show that, for a Sturm-Liouville equation with a general integrable potential, if its weight is a positive linear combination of $n$ Dirac Delta functions, then it has at most $n$ (may be less than $n$, or even be $0$) distinct real Dirichlet eigenvalues, or every complex number is a Dirichlet eigenvalue; in particular, under some sharp condition, the number of Dirichlet eigenvalues is exactly $n$. Our main method is to introduce the concepts of characteristics matrix and characteristics polynomial for Sturm-Liouville problem with Dirac weights, and put forward a general and direct algorithm used for computing eigenvalues. As an application, a class of inverse Dirichelt problems for Sturm-Liouville equations involving single Dirac distribution weights is studied. It is a joint work with Prof. Jiangang Qi.

报告人简介：陈潇，2016年毕业于南开大学陈省身数学研究所，获理学博士。2016-2018年于山东大学威海校区数学与统计学院做博士后，2018年至今留校工作，现任讲师，硕士生导师，发表SCI收录的学术论文8篇，主持完成国家级和省部级基金各一项，研究方向为算子代数、抽象调和分析以及微分算子谱理论。