算子理论与算子代数及其应用短课程

报告题目：Reproducing Kernel Hilbert Spaces and Complete Nevanlinna-Pick Property

报告人：储成 教授

报告时间：2022年8月9日、10号上午9：00-11：00

腾讯会议：772-4637-3793

邀请人：杨义新 教授

报告摘要：The original Pick problem is to determine if a finite sequence of points in the unit disk can be mapped to a sequence of complex numbers using a holomorphic function bounded by 1. We discuss a necessary and sufficient condition to solve the Pick problem in a view of reproducing kernel Hilbert spaces, which leads to the complete Nevanlinna-Pick property. In this talk, we start with presenting the general theory of reproducing kernel Hilbert spaces and background of the Pick problem. Then we introduce reproducing kernel Hilbert space with complete Nevanlinna-Pick kernel. It includes Hardy spaces and Dirichlet spaces. We will discuss two questions:

1. Which Hardy space properties can be generalized to spaces with complete Nevanlinna-Pick kernel?

2. Which spaces have complete Nevanlinna-Pick kernel?

报告人简介：储成，博士毕业于Washington University in St. Louis, 后于Vanderbilt University, Laval University 做博士后。研究兴趣包括: 复分析，算子理论，再生核等。 研究工作发表在 J. Funct. Anal., Bull. Lond. Math. Soc., Indiana Univ. Math. J., J. Math. Anal. Appl等数学刊物上。