Abstract. In this article, we study tensor product of Hilbert C∗-modules and Hilbert spaces. We show that if E is a Hilbert A-module and F is a Hilbert B-module, then tensor product of frames (orthonormal bases) for E and F produce frames (orthonormal bases) for Hilbert A⊗B-module E ⊗F , and we get more results. For Hilbert spaces H and K, we study tensor product of frames of subspaces for H an...

The deepest and most difficult question in Fusion Frame Theory is the construction of fusion frames with added properties for specific applications. In frame theory we have a powerful tool introduced by Benedetto and Fickus [1] called frame potentials (See [5] for a deep analysis of frame potentials). Frame potentials are a valuable tool for showing the existence of frames with certain specifie...

This paper gives a perturbation theorem for frames in a Hilbert space which is a generalization of a result by Casazza and Christensen. Then this result is applied to the Perturbation of regular sampling in shift-invariant spaces. Irregular sampling theorems for frames in wavelet subspaces are established for which it is easy to derive explicit formulas and algorithms to calculate the ranges of...

Given a real and invertible d×d matrix C, we define for k ∈ Zd a generalized translation operator TCk acting on f ∈ L 2(Rd) by (TCkf)(x) = f(x − Ck), x ∈ R . A generalized shift-invariant system is a system of the type {TCjkφj}j∈J,k∈Zd , where {Cj}j∈J is a countable collection of real invertible d×d matrices, and {φj}j∈J ⊂ L 2(Rd). Generalized shift-invariant systems contain the classical wavel...

If ψ is a BLc wavelet, a Chui-Shi family of redundant tight frames {Ψ(k); k ∈ Z} can be built. Its redundancy is studied through the subspaces of coefficients in l2(Z2). It will be proved that these subspaces converge to zero when ψ is a uniformly continuous wavelet. Also a Whittaker-ShannonKotel’nikov type sampling theorem will be given for discrete vector functions associated to Ψ(k). Even mo...

For any fixed fusion frame, its optimal dual fusion frames for reconstruction is studied in case of erasures of subspaces. It is considered that a probability distribution of erasure of subspaces is given and that a blind reconstruction procedure is used, where the erased data are set to zero. It is proved that there are always optimal duals. Sufficient conditions for the canonical dual fusion ...

The concept of a generalized quarternary multiresolution struccture (GQMS) of space is formulated. A class of multiple affine quarternary pseudoframes for subspaces of 2 4 ( ) L R are introduced. The construction of a GQMS of Paley-Wiener subspaces of 2 4 ( ) L R is studied. The sufficient condition for the existence of pyramid decomposition scheme is presented based on such a GQMS. A sort of a...