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T_fk，T_gk的Toeplitz算子，其中假设g_k=g₁^(k)+g₂^(k)，g₁^(k)=a_j^(k) z^j，g₂^(k)=b_j^(k)z^j∈H^∞(D)；f_k∈L^∞(D,dA)。f_k(re^iθ)=f_p^(k)(r)e^ipθ(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 T_fk, T_gk in Bergman space. In case g_k=g₁^(k)+g₂^(k), g₁^(k)=a_j^(k) z^j, g₂^(k)=b_j^(k)z^j∈H^∞(D); f_k∈L^∞(D,dA). f_k(re^iθ)=f_p^(k)(r)e^ipθ(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).