Let H be a Hilbert space. Given a bounded positive definite operator S on H, and a bounded sequence c = {ck}k∈N of non negative real numbers, the pair (S, c) is frame admissible, if there exists a frame {fk}k∈N on H with frame operator S, such that ‖fk‖ 2 = ck, k ∈ N. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended ver...

Generalized fusion frame and some of their properties in tensor product Hilbert spaces are described. Also, the canonical dual g-fusion is considered. Finally, operator for a pair Bessel sequences presented.

In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literature on this topic.

This paper is an examination of techniques for obtaining Fourier series-like expansions of finite-energy signals using so-called Gabor and wavelet expansions. These expansions decompose a given signal into time and frequency localized components. The theory of frames in Hilbert spaces is used as a criteria for determining when such expansions are good representations of the signals. Some result...