Tight K-g-Frame and Its Novel Characterizations via Atomic Systems

Abstract

K-g-frame is a generalization of g-frame. We generalize the tight g-frame to K-g-frame via atomic systems. In this paper, the definition of tight K-g-frame is put forward; equivalent characterizations and necessary conditions of tight K-g-frame are given. In particular, the necessary and sufficient condition for tight K-g-frame being tight g-frame is obtained. Finally, by means of methods and techniques of frame theory, several properties of tight K-g-frame are given.