报告题目：On the Phases of Sectorial Operators

报 告 人： 于天秋 教授 (黑龙江大学)

报告时间： 2022年8月22日 上午9:00-10:00

报告地点：腾讯会议 会议ID：605-998-148

邀 请 人：刘浏 教授

报告摘要 ： In this talk, we first define the phases of a sectorial operator based on the numerical range. Motivated by the classical small gain theorem, we formulate an operator small phase theorem for the invertibility of I+AB of two sectorial operators A and B, which plays a crucial role in feedback stability analysis. In particular, we consider the class of sectorial operators, which are the sum of a strictly positive and compact operator with closed numerical ranges lie in the open right half plane. More properties of the phases for those operators are studied, including those of compressions, Schur complements, and operator sums. Further, we establish a majorization relation between the phases of the spectrum of AB and the phases of two sectorial operators A and B.

报告人简介： 于天秋，黑龙江大学教授，硕士生导师。2011年毕业于吉林大学基础数学专业，获博士学位。先后在大连理工大学和香港科技大学从事合作研究。研究方向为: 时变系统的鲁棒控制，扇形算子的相位。主持国家自然科学基金2项，省基金1项。 主要研究成果先后发表在《SIAM Journal on Control and Optimization》， 《Proceedings of the American Mathematical Society》，《Systems & Control Letter》等国际期刊。