Bergman空间上的Toeplitz算子的乘积有限和问题

The Finite Sum Problem of the Product of Toeplitz Operators on Bergman Spaces

本文讨论了Bergman空间上两个形如Tfk,Tgk的Toeplitz算子,其中假设gk=g1(k)+g2(k),g1(k)=aj(k) zj,g2(k)=bj(k)zj∈H∞(D);fk∈L∞(D,dA)。fk(reiθ)=fp(k)(r)eipθ(1≤k≤N)。探究Toeplitz算子Tfk,Tgk的有限乘积有限和的相关问题,分析计算得到了其为零算子的一个必要条件。

This paper discusses two Toeplitz operators as Tfk, Tgk in Bergman space. In case gk=g1(k)+g2(k), g1(k)=aj(k) zj, g2(k)=bj(k)zj∈H∞(D);fk∈L∞(D,dA). fk(reiθ)=fp(k)(r)eipθ(1≤k≤N). This paper explores the related problems of the sum of the finite products of the two Toeplitz operators as Tfk, Tgk under a large amount of data and calculations. A necessary condition of zero operator is obtained (N).