Discretization of continuous frame

Abstract

In this paper we consider on the notion of continuous frame of subspace and define a new concept of continuous frame, entitled {\it continuous atomic resolution of identity}, for arbitrary Hilbert space $\h$ which has a countable reconstruction formula. Among the other result, we characterize the relationship between this new concept and other known continuous frame. Finally, we state and prove the assertions of the stability of perturbation in this concept.