Analysis Seminar: "Trace formulas for semi-commutator of Toeplitz operators and their generalizations"

Abstract: We obtain formulas about the reproducing kernels of the Hardy, weighted Bergman, and Fock spaces that leads to a series of applications. One of the applications is an explicit trace formula for semicommutators T_fT_g-T_{fg} on the disk. Comparing to the Helton-Howe trace formula, we also discuss about the higher-dimensional generalization of the semi-commutator formula. Our formulas can also be used to study Toepliz quantization. This is joint work with Xiang Tang and Dechao Zheng.

Host: Xiang Tang