Given a frame for a subspace W of a Hilbert space H, we consider a class of oblique dual frame sequences. These dual frame sequences are not constrained to lie in W . Our main focus is on shift-invariant frame sequences of the form {φ(· − k)}k∈Z in subspaces of L2(R); for such frame sequences we are able to characterize the set of shift-invariant oblique dual Bessel sequences. Given frame seque...

The main purpose of the paper is to give a characterization all compactly supported dual windows Gabor frame. As an application, we consider iterative procedure for approximation canonical window via on every step. In particular, allows have from certain modulation spaces or Schwartz space.

This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis are made by two frames, respectively. The goal is to give some results about localization spectra identify regions complex plane containing using information symbols.

We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group. This has applications to shift-invariant spaces and wavelet theory. One of the main findings in this paper is that whenever a shift-invariant subspace in L2(R...

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 ...