The Stability Of Fusion Frames And Fusion-Riesz Frames

In 1952, Duffin and Schaeffer firstly introduced the concept of frame when they studied some problems in nonharmonic Fourier series. The concept of frame was reintroduced in 1986 by Daubechies, Grossmann and Meyer and popularized from then on. So far, there have been a series of important results in frame theory that plays an important role in filter bank theory, sigma-delta quantization, signal and image processing, and many other fields.As a generalization of frames, fusion frames (or frames of subspaces) were considered recently by Casazza and Kutyniok, Fornasier. At present, many important results of fusion frames have been obtained by some authors. But there are still some problems to be solved, such as the perturbation of operator about fusion frames and fusion-Riesz frames. So, in this paper, we mainly study the perturbation of operator about fusion frames and fusion-Riesz frames. We generally arrange the text structure as follows:In chapter 1, firstly, we make an introduction about the generation and development of frame theory. Secondly, we recollect some basic concepts and properties of frame and fusion-frames. Lastly, we list the main works of this paper.In chapter 2, firstly, we give some results of the operator perturbation of fusion frames. Our results generalize and improve the remarkable results which have been obtained by Casazza, Kutyniok, Gavruta, etc. Secondly, we point out the relationships among some results which have been obtained by other scholars. Lastly, we consider the effect of weight set on the operator perturbation of fusion frames in Hilbert spaces.In chapter 3, we make use of some properties of the gap between two closed subspaces to study the operator perturbation of fusion-Riesz frames, and obtain some new results. In addition, we consider the effect of weight set on the operator perturbation of fusion-Riesz frames in Hilbert spaces.