学术报告

报告人：Caixing Gu

报告题目2：Composition and multiplication operators on the derivative Hardy space  S^2(D)

报告内容： We propose a different (and equivalent) norm on S^2(D) which consists of functions whose derivatives are in the Hardy space of unit disk. The reproducing kernel of S^2(D) in this norm admits an explicit form, and it is a complete Nevanlinna-Pick kernel. Furthermore, there is a surprising connection of this norm with 3-isometries. We then study composition and multiplication operators on this space. Specifically, we obtain an upper bound for the norm of $C_{\varphi}$ for a class of composition operators. We completely characterize multiplication operators which are m-isometries. As an application of the 3-isometry, we describe the reducing subspaces of $M_{\varphi}$ on S^2(D) when $\varphi$ is a finite Blaschke product of order $2$.

报告人简介：Caixing Gu is a Professor of Department of Mathematics

at California Polytechnic State University San Luis Obispo. His research interests include: Toeplitz and Hankel operators on function spaces, mlti-isometries, H^{\infty} control theory on Hilbert spaces.

报告时间：2017年7月6日（星期四） 上午 10:10-11:10 创新园大厦A1101

校内联系人：卢玉峰  电话：84708352