摘要
主要研究调和Hardy空间上对偶Toeplitz算子的代数性质及谱包含定理.首先,给出多圆环Tn上的调和Hardy空间的定义.然后,证明了有界符号的对偶Toeplitz算子可逆当且仅当其符号可逆,进而刻画了对偶Toeplitz算子的谱包含定理,基于谱包含定理描述了对偶Toeplitz算子的自伴性、正性与符号函数的关系.最后,研究了调和Hardy空间上的对偶Toeplitz算子的交换性:证明出两个解析或者余解析的对偶Toeplitz算子可交换.相对于Hardy空间,调和Hardy空间的调和性使交换性的研究变得尤为复杂,因此一般符号的对偶Toeplitz算子交换性很难画.只给出n=2时,一些特殊符号的对偶Toeplitz算子可交换的充分必要条件.
In the current field of mathematics,there are only few theories of dual Toeplitz operators on harmonic Hardy space,since it is always about Hardy space,Bergman space,even harmonic Bergman space.The harmonic Hardy space on Tnis introduced in this paper.This paper is divided into three parts.The harmonic Hardy space on Tnis introduced firstly in this paper.Then we start an investigation of dual Toeplitz operator and obtain a spectral inclusion theorem.There are some corollaries introduced after the proof of the spectral inclusion theorem.Commuting dual Toeplitz operator is characterized in the last part.Some main properties are displayed.Through a simple example,we can know the importance of the harmonicity.So we can not get a theory for all operators.In this paper,we only study the situation hat n=2,and they symbol function a special form.
出处
《辽宁师范大学学报（自然科学版）》
CAS
2016年第3期289-294,共6页
Journal of Liaoning Normal University:Natural Science Edition
基金
国家自然科学基金资助项目(11271059)
