报告题目：Sub-Bergman Hilbert Spaces in the Unit Disk

报告时间：2023-04-21  16:00-17:00

报告人：朱克和 教授  纽约州立大学

报告地点：理学院东北楼四楼报告厅

报告摘要：Let H₁^∞ denote the closed unit ball of the algebra of bounded analytic functions on the unit disk D. For φ∈H₁^∞ consider the defect operators D_φ and D_{φ ̅}  for the Toeplitz operators T_φ and T_φ*, respectively, on the weighted Bergman space A_α². The ranges of D_φ and D_{φ ̅} , denoted by H(φ) and H(φ ̅) and equipped with appropriate inner products, are called sub-Bergman spaces.

　I will talk about the relatively new theory of sub-Bergman (and sub-Hardy) Hilbert spaces, including their reproducing kernels, the compactness of the defect operators, and the identification of H(φ) and H(φ ̅) with more familiar function spaces. For example, when α>-1, we have H(φ)=H(φ ̅ )=A_α-1² if and only if φ is a finite Blaschke product. Part of the talk is based on recent joint work with Shuaibing Luo of Hunan University.