Speaker: Wang Yi, Postdoctoral fellow, Department of Mathematics, Vanderbilt University

Date: Aug. 25, 2021

Time: 9:00

Location: Tencent Meeting, ID:723 763 131

Sponsor: School of Mathematics, Shandong University

Abstract:

Using a variant of the Bochner-Martinelli formula, we obtain formulas involving reproducing kernels of the weighted Bergman spaces and the Hardy space. As an application, we obtain explicit formulas of the trace of semicommutators T_fT_g-T_fg on these spaces. Also, an explicit formula for the Toeplitz quantization and Berezin quantization on the unit ball is obtained. We also prove that, analogous to the Helton-Howe trace formula, a partial antisymmetrization of 2n Toeplitz operators with smooth symbols is in the trace class. Then we give the limit of the trace.

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https://www.view.sdu.edu.cn/info/1020/155739.htm