Study Of Some Questions For Frame Sequences And Approximately Dual Frames

The concept of frame was firstly introduced in by Dufn and Schaefer when they werestudying nonharmonic Fourier series in the fifties of the twentieth century. Every elementin a Hilbert space can be represented by the frame, but the way of representation is notunique. It also has many extensive applications in signal processing, data compression,communication and so on. The research contents of frame theory mainly include: framecharacters, dual frame characters, perturbation of frame sequence, etc. This thesis ismainly to discuss frame sequences perturbation and approximately dual frames. Thisthesis consists of four chapters.Chapter1states the origin of frame concepts and sketches the structure and worksof the thesis.Chapter2lists some basic theorems to be used throughout the thesis, and the con-cepts of frames and frame sequences.Chapter3is one of the main contents. On the basis of known frame sequencesperturbation results, combined with the operator theory, we obtain the more generalresults of frame sequences perturbation.Chapter4is another main content. First give the concept of approximately dualframe. Then mainly discussion is the following question: if we can find a framethat is close to and for which it is possible to find a dual frame, doesit follow that is an approximate dual ofn addition, approximatelydual frame characters are also given.