双圆盘加权Dirichlet空间上Toeplitz算子的约化子空间  

Reducing Subspaces of Toeplitz Operator on the Weighted Dirichlet Space of the Bidisk

作　　者：林鸿钊[1,2] 胡寅寅[1] 卢玉峰[1] LIN Hongzhao HU Yinyin LU Yufeng(School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China College of Computer and Information Sciences, Fujian Agriculture and Forestry University, ~zhou 350002, China 2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, Chin 3Corresponding author. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China.)

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024 [2]福建农林大学计算机与信息学院,福州350002

出　　处：《数学年刊（A辑）》2016年第3期311-328,共18页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11271059)的资助

摘　　要：刻画了双圆盘加权Dirichlet空间D_α(D^2)上Toeplitz算子T_Z_1N(或T_z_2N)和T_z_1N_z_2N的约化子空间.结果表明Toeplitz算子T_z_1N(或T_z_2N)的约化子空间结构与权系数α无关,而Toeplitz算子T_2_1N_z_2N的约化子空间结构与权系数α有关.In this paper,the authors describe the reducing subspaces of Toeplitz operators T_z_1n（or T_z_2n） and T_z_1N_z_2N on the weighted Dirichlet space of the bidisk D_α（D^2）.They show that the structure of the reducing subspaces of T_z1N（or T_z_2N） is independent of the weightα,while for T_z_1N_z^2N,the situation is different.

关 键 词：约化子空间 TOEPLITZ算子 DIRICHLET空间 双圆盘 

分 类 号：O177[理学—数学]