Spectra And Complex Symmetric Of Weighted Composition Operators On Hilbert Spaces Of Holomorphic Functions

Composition operators and weighted composition operators play critical roles on varieties kinds of function spaces.In this paper,we mainly investigate the spectra and the complex symmetric of(weighted)composition operators acting on the classical Hardy-Hilbert space and several other function spaces.This properties of(weighted)composition operators remain much to be done on both methods and results.In this paper,we will give answers to several open questions.Firstly,we will discuss the spectra and their structures of weighted composition operators acting on Hardy space.In Chapter 2,we will investigate the spectra of in-vertible weighted composition operators:we will get a complete result by solving an open question posed in several other papers.And in Chapter 3,we will consider the noninvertible ones,and also get a complete result.Then in Chapter 4,we will discuss the complex symmetric of composition op-erators acting on Hardy space:we will prove that there is no other linear fractional mappings can induce a complex symmetric composition operator except for the ones already known by people.by doing this,we gives a complete description of the com-plex symmetric composition operators induced by linear fractional mappings.Finally in Chapter 5 and Chapter 6,we will generalize our results to the weighted Bergman spaces and the function spaces of several complex varieties.