K-frames In A Hilbert Space

Theory of frames in a Hilbert space is one of the most important part in wavelet analysis and has many important practical applications. In recent years, various results on Frame Theory have been developed. In this paper,K-frames and K-Bessel sequence in a Hilbert space are introduced and discussed, which are based on the study of frames and Bessel sequences in a Hilbert space, and some new properties are obtained.This paper is organized as follows:In Chapter 1, we introduce the background and the research status of frame theory, the major work and organization of this paper are given in brief.In Chapter 2,K-frames and K-Bessel sequence in a Hilbert space are introduced and discussed, relationships between frames and K-frames are given.In Chapter 3, using the inflation of frames, several inflation forms of K-frames and K-Bessel sequence in a Hilbert space are discussed.