The Properties Of Frames And Generalized Frames In Hilbert Space

Frames for Hilbert space were formally defined by R.J.Dufnn and A.G.Schaeffer in 1952. They play an important role in the development of wavelet analysis. Frames for Hilbert space can be viewed as generalized bases for if. It is very important in practice to study frames. Functional analysis as an ancient branch of mathmatics is a powerful tool in studing area. In this thesis, we give some results about frames and generalized frames.This thesis consists of four chapters.In chapter 1, we introduce the develepment of frames and the populor ways in studing frames.In chapter 2, we introduce some concepts such as Bessel sequence, frame, Riesz frame, pre-frame operator, frame operator and some basic properties of them. At the same time, we study the stability of frame and frame sequence.In chapter 3, we study the approximation of the solution to moment problem by means of finite subsets of the frame.In chapter 4, we introduce some concepts such as Bessel sets, generalized frame, pre-frame operator, frame operator and some basic properties of them. Making use of spectral theorem, we study the stability of generalized frame and independent frame.