走向现代数学学术报告 - 杨义新教授 （No. 519）

报告题目：The compressed shift operators on Hardy space over the bidisk

报告人：杨义新 教授（大连理工大学）

报告时间：2022年5月25日 ，10：00

报告地点：腾讯会议 472755243

报告摘要：The model operators $S(u)$ have played an important role in developing both function and operator theory over the past century. In particular, the lattice of invariant subspaces and the spectrum of $S(u)$ have been very well understood. This success led people to study the Hardy space over the bidisk. We are interested in the independent behavior of compressed shift operator $S_{z}$ on the Beurling type quotient modules induced by rational inner functions. In this talk, we characterize when is $S_z^*$ a Cowen-Douglas operator and extend the notion of Cowen-Douglas operator to be the generalized Cowen-Douglas operator. The connection between the reducibility of $S_z$ and generalized Cowen-Douglas operator are established.

报告人简介：杨义新，大连理工大学数学科学学院教授、博士生导师，2015年于纽约州立大学奥尔巴尼分校获博士学位。主要从事泛函分析、算子理论与算子代数的教学和科研工作，包括双圆盘Hardy空间上的算子理论、双圆盘上的Nevanlinna-Pick（广义）插值等。在《J. Funct. Anal.》、《Integr. Equ. and Oper.Theory》等学术期刊上发表科研论文多篇，目前主持国家自然科学基金面上项目一项。