Study Of Generalized Bessel Multipliers And Related Problems

In 1952, R. J.Du?n and A. C. Schae?er introduced the concept of frame for Hilbertspace in order to study some deep problems in nonharmonic Fourier series. Frame theoryhas promptly developed after wavelet analysis's appearance.It has been widely usedsignal processing, image processing, numberical calculation, and so on. This thesis ismainly to discuss g-Bessel multipliers,and consists of ?ve chapters:Chapter 1 brie?y introduces the background of wavelet analysis, frames theory,andsketches the main works and the structure of the thesis.Chapter 2 the de?nition of frame and some operators associated with frames aregave, the characterizations of frames and some operators associated with frames areintroduced.Chapter 3 the de?nition of g-frame and some operators associated with g-frame aregave, and the characterization of g-frames and some operators associated with g-frameare listed.Chapter 4 is main contents. First, the de?nition of g-Bessel multipliers is gave,and then, the characterizations of Sm are discussed, at last, the characterizations ofg-Bessel multipliers are analysed.In the last chapter, The de?nition of weighted g-frames is given and some basicproperties of weighted g-frames are proved, Moreover, a relationship between weightedg-frames and g-frames multipliers is investigated.