F²(Cⁿ)空间上无界的复对称加权复合算子  

Unbounded Complex Symmetric Weighted Composition Operators on F2(Cn) Space

作　　者：黄周萍 

机构地区：[1]华南农业大学,广东 广州

出　　处：《理论数学》2021年第8期1493-1504,共12页Pure Mathematics

摘　　要：本文研究了n维Fock空间上加权复合算子TψDθkf:=ψ⋅f(k)。θ关于共轭(Jf)(z)=(C1,0,c)f(z)=cf(z)的复对称性和自伴性,其中θ和ψ是Cn上的两个整函数,k是非负整数,得出了算子TψDθk是J-自伴的等价刻画。此外,我们还给出了TψDθk是厄米特算子的充要条件。In this paper, we study the complex symmetry and self-adjoint of the conjugate (Jf)(z)=(C1,0,c)f(z)=cf(z) by the weighted complex operator TψDθkf:=ψ⋅f(k)。θ on n dimensional Fock space, where θ and ψ are two entire functions, k is a nonnegative integer. We give an equivalence characterization where the operator TψDθk is a J-self-adjoint. In addition, we prove that the unbounded maximal weighted composition operator is self-adjoint.

关 键 词：F²(Cⁿ)空间 复对称性 加权复合算子 自伴性 

分 类 号：O17[理学—数学]