Toeplitz算子的乘积  

Products of Toeplitz operators

作　　者：王春梅[1] 葛斌[2] 

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080 [2]哈尔滨工程大学理学院,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2017年第6期666-670,共5页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省教育厅科学技术研究项目(12541618)

摘　　要：考虑由对称测度定义的解析函数Hilbert空间上的Toeplitz算子的乘积问题。在一般的由对称测度定义的函数空间上,得到结论:如果T_fT_g=Th,其中f,g,h是开单位圆盘上的有界调和函数,且f,g不是常值函数,那么若f和g中有一个是解析的,则另一个也是解析的;若f和g中有一个是共轭解析的,则另一个也是共轭解析的。对一特殊的对称测度定义的函数空间,得到结论:T_fT_g=Th成立的充要条件是平凡的,其中f,g,h是开单位圆盘上的有界调和函数。Consider the product problem of Toeplitz operators on the Hilbert spaces of analytic functions with symmetric measures. First, it is proven on function spaces with symmetric measures that if TfTg = Th, where f, g and h are all bounded harmonic functions on the open unit disk, and thatfand g are not constant functions, then, if at least one off and g is analytic, the other one is also analytic ; if at least one off and g is conjugate analytic, the other one is also conjugate analytic. Second, it is proven that, on the function space with a special symmetric measure, the necessary and sufficient condition of TfTg = Th is trivial, here f, g, h are all bounded harmonic functions on the open unit disk.

关 键 词：对称测度 TOEPLITZ算子 调和函数 

分 类 号：O177[理学—数学]