On The Stability Of Frames For Hilbert Spaces

Wavelet Analysis is an important branch of Applied Mathematics. Theory of frames is an important part of Wavelet Analysis, and the stability of frames takes an important part in the study of frames.In this article, we mainly study the stability of frames for Hilbert spaces, including the stability of general frames and that of two important classes of frames. And we take much attention to wavelet frames. Furthermore, we study the conjugate linear operators on Hilbert spaces and normed spaces. We divide the article into three chapters as follows:In Chapter 1, we mainly discuss the stability of general frames. At first, we recall the definitions and the characterazitions of Bessel sequences, frames and frame operators and give some equivallent chracterizations of them. We then study the stability of frames and obtain a foundation of the following study on Gabor frames and wavelet frames.In Chapter 2, we study the stability of Gabor frames and wavelet frames. Some sufficient and necessary conditions for them are given. We discuss the stability of these frames and obtain some results.In Chapter 3, we study the conjugate linear operators on Hilbert spaces and normed spaces. A series of important properties of these operators are obtained, some relationships between conjugate linear operators and linear ones are also discussed.