The Researches Of Composition Operators Theory On The Dirchlet Series Space

This paper mainly discusses the properties of composition operators on the Dirich-let series Hardy space.The thesis is divided into four chapters.The first chapter is the introduction of basic knowledge and background material.There have five basic oper-ators are introduced,and with important conclusions related to each operator are given,and the proof process is also given.The second chapter gives the definition and con-vergence of Dirichlet series,which is the base of reading and proof of the third chapter.The third chapter is referring to the content of[17],we optimize the process and logic of theorem proving and correct some theorems proving on the basis of the original paper,which makes the proof more simple and understandable.In Chapter four,we mainly introduce the theory of compact composition operators,mainly in order to let readers understand the theory of composite operators further.This kind of composition operator research is widely used in complex analysis and complex dynamical systems.In the research of ergodic theory and unification theory,studying the properties of composition operators can help us to study related courses and topics more profoundly.