g-frames and stability of g-frames in Hilbert spaces - Najati, A.; Faroughi, M. H.; Rahimi, A. (Methods of Functional Analysis and Topology, 2008)
Wenchang Sun in his paper [Wenchang Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322 (2006), 437–452] has introduced g-frames which are generalized frames and include ordinary frames and many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. In this paper we develop the g-frame theory for separable Hilbert spaces and give characterizations of g-frames and we show that g-frames share many useful properties with frames. We present a version of the Paley-Wiener Theorem for g-frames which is in spirit close to results for frames, due to Ole Christensen.