Invariant Subspace Of Composition Operators On Spaces Of Analytic Functions

In this thesis,we mainly consider the invariant subspace of composition operators C? on Hardy space Hp in space of analytic function where the composition operators C? corresponding to the induction function ? that is a analytic self-map of D.This thesis will study invariant subspace from three aspects.Firstly,we discuss invariant subspace of composition operators C? on subspace H?,?p of Hardy space Hp.We will explore the various forms of invariant subspaces of C?.Secondly,we consider Beurling type invariant subspace of C?.When ? is a inner function,we prove that ?Hp is invariant for C? if and only if(?)belongs to S(D)and S(D)is schur class.Thirdly,we obtain that zn Hp is nontrivial invariant subspace for Deddends algebras DC? when C? is a compact composition operator and ? satisfies that ?(0)=0 and ????<1.This thesis mainly studies from the above three perspectives,and also reach the related conclusion of automorphism and invertible map.