双圆盘商模Nψ上Toeplitz算子的向量丛模型  

A Vector Bundle Model of Toeplitz Operators on the Quotient Module Nψ in the Bidisc

作　　者：许安见 邹杨 XU An-jian;ZOU Yang(School of Science,Chongqing University of Technology,Chongqing 400054,China;Department of Mathematics and Information Project,Chongqing University of Education,Chongqing 400067,China)

机构地区：[1]重庆理工大学理学院,重庆400054 [2]重庆第二师范学院数学与信息工程学院,重庆400067

出　　处：《西南大学学报（自然科学版）》2021年第4期79-84,共6页Journal of Southwest University(Natural Science Edition)

基　　金：重庆市科学技术委员会项目(cstc2018jcyjA2248,cstc2019jcyjX0295);重庆市教育委员会项目(KJQN201801110,KJQN202001606);国家自然科学基金项目(11871127);重庆第二师范学院校内项目(KY201703A).

摘　　要：设D为复平面上的开单位圆盘,H 2(D 2)为双圆盘D 2上的Hardy模,ψ(z 2)为D上的有限Blaschke乘积.首先定义了H 2(D 2)的Nψ-商模,利用Blaschke积的性质给出了商模的等价刻画,然后根据等价刻画构造出商模的一组正交正规基,并给出Nψ-商模的具体刻画.最后研究了Nψ-商模上以有限Blaschke乘积B(z 1)为符号的解析Toeplitz算子T B(z 1),通过分析B(z 1)的全体逆的结构,建立了T B(z 1)的Bergman向量丛模型,并根据该模型给出了该Toeplitz算子的一些性质的几何刻画.Let D be an open unit disc in the complex plane,H 2(D 2)the Hardy module on the bidisc D 2,andψ(z 2)a finite Blaschke product.Firstly,the Nψ-quotient module of H 2(D 2)is defined,and an equivalent characterization of the quotient module Nψis given by the properties of a finite Blaschke product.Secondly,an orthonormal basis is constructed according to this equivalent characterization and a more concrete characterization of Nψis given.Finally,the analytic Toeplitz operators on Nψ-quotient module with the finite Blaschke product B(z 1)as symbols are studied,and a Bergman bundle shift model is constructed by investigation of the set of inverses of B(z 1).Furthermore,the geographical characterization of some properties of the Toeplitz operator is given using this model.

关 键 词：TOEPLITZ算子 BERGMAN空间 HARDY空间 商模 

分 类 号：O177.1[理学—数学]