K-frames For Unitary Systems In Hilbert Spaces

K-frames are the generalization of the frames. In this thesis, we first generalize the frames for unitary systems to K-frames in Hilbert spaces and introduce the definition of the K-frame vectors. By establishing the correlations between the complete wandering vectors and the Parseval K-frame vectors, some properties about the Parseval K-frame vectors are given. In the second, we investigate the K-frame vectors which are unitarily equivalent. Furthermore, for the unitary representation of the K-frame vectors, by using the analysis operators and operator K, we get some conclusions concerning on the K-frame multiplicity. Finally, we give the definition of the multi- K-frame vectors, of which some properties are characterized.