一类新型全纯函数空间上加权复合算子的研究

复合算子是算子理论中极为重要的研究对象，全纯函数空间上复合算子的研究与许多数学分支有着密切联系。目前此领域研究的底空间多为经典的函数空间，如Hardy空间、Bergman空间、Dirichlet空间、Fock空间等。本课题主要研究整Dirichlet级数构成的Hilbert空间上加权复合算子相关性质的刻画，如有界性、复对称性、复正规性和m-复对称性等，并探讨此类新型全纯函数空间上加权复合算子复对称性、复正规性与正规性之间的关系。从而建立算子性质与符号函数的内在联系，丰富和完善算子论和函数论的研究内容。

The composition operator is a very important research object in operator theory. The study of composition operator on holomorphic function space is closely related to many mathematical branches. At present, most of the base spaces studied in this field are classical function spaces, such as Hardy spaces, Bergman spaces, Dirichlet spaces, Fock spaces, etc. This project mainly studies the characterizations of some properties of weighted composition operators on Hilbert spaces of entire Dirichlet series, such as boundedness, complex symmetry, complex normality and m-complex symmetry, and discusses the relationship between complex symmetry, complex normality and normality of weighted composition operators on such new holomorphic function spaces. Thus, the internal relationship between operator properties and symbol functions is established, and the research contents of operator theory and function theory are enriched and improved.