Fock空间上径向函数诱导的Toeplitz算子

Toeplitz Operators with Radial Symbols on Fock Space

本文讨论了Fock空间上以径向函数和拟齐次函数为符号的Toeplitz算子的代数性质,给出了两个以径向函数为符号的Toeplitz算子的积仍为Toeplitz算子的充分必要条件,并且研究了以拟齐次函数为符号的Toeplitz算子的交换性.

We discuss some algebraic properties of Toeplitz operators with a class of radial and quasi-homogeneous symbols on the Fock space of the complex plane. We give necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator, and study the zero-product problem of several such Toeplitz operators. Furthermore, the corresponding commuting problem of Toeplitz operators with quasi-homogeneous symbols is studied.