G-Frames, Fusion Frames and the Restricted Isometry Property

Mohammad Sadegh Asgari, Golsa Kavian

Abstract

In this paper we study the restricted isometry property for $g$-frames, we will show how to use tight $g$-frames that have the restricted isometry property to construct fusion frames. We also study the conditions which under removing some element from a $g$-frame, again we obtain another $g$-frame so that Theorem 4.3 obtained in [M.S. Asgari, On the stability of fusion frames (frames of subspaces), Acta Math. Sci. (Ser. B) 31 (4) (2011) 1633--1642] is a special case of it.