Study Of The Frames And Their Related Operators In Hilbert Space

This master's thesis mainly consists of four chapters. In chapter one we introduced the study work of the frames and operators provided by Daubechies, Peter G Casazza and Ole Christensen, we also introduced the study on frames and operators in our country, and the mainly conclusion of this master thesis. In chapter two, on the basis of further characters of the frames we provided two frame decomposition formulas. In chapter three we mainly studied the pseudo-inverse operator and the frame in Hilbert space. Firstly, we provided some characters of the pseudo-inverse operator in Hilbert space, and prove the following proposition: Let U be a bounded operator with closed range. Then(U(?)U)(?) = U(?)U(?); We also provided some relations between the inverse operator and the pseudo-inverse operator of the frame. Then we got the general decomposition of the frames. In chapter four, we studied some characters of the strong frame, and provided several conditions of frame coefficient approximation. Those conditions simplified the results of Ole Christensen in his document (14) .