G-frame representations with bounded operators

摘要

Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form {T(i-1)f(1)}(i is an element of N), where f(1) belongs to Hilbert space H and T : H -> H belongs to certain classes of bounded operators. Christensen et al. studied frames for H with index set N (or Z), that has representations in the form {T(i-1)f(1)}(i is an element of N) (or {T(i)f(0)}(i is an element of Z)). As frames of subspaces, fusion frames and generalized translation invariant systems are the special cases of g-frames, the purpose of this paper is to study and get sufficient conditions for g-frames Lambda = {Lambda(i) is an element of B(H, K) : i is an element of N (or Z)} having the form Lambda(i+1) = Lambda T-1(i), T is an element of B(H) (or Lambda(i+1) = Lambda T-0(i), T is an element of GL(H)). Also, we get the relation between representations of dual g-frames with index set Z. Finally, we study stability of g-frame representations under some perturbations.