A Gabor or Weyl-Heisenberg frame for L2(Rd) is generated by time-frequency shifts of a square-integrable function, the Gabor atom, along a time-frequency lattice. The dual frame is again a Gabor frame, generated by the dual atom. In general, Gabor frames are not stable under a perturbation of the lattice constants; that is, even for arbitrarily small changes of the parameters the frame property...

We use a generalization of Wiener’s 1/f theorem to prove that for a Gabor frame with the generator in the Wiener amalgam space W (L∞, ` )(R), the corresponding frame operator is invertible on this space. Therefore, for such a Gabor frame, the generator of the canonical dual belongs also to W (L∞, ` )(R).

BACKGROUND, AIMS AND DESIGN The increase in mobile telephone-only households may be a source of bias for traditional landline gambling prevalence surveys. Aims were to: (1) identify Australian gambling participation and problem gambling prevalence using a dual-frame (50% landline and 50% mobile telephone) computer-assisted telephone interviewing methodology; (2) explore the predictors of sample...

Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals with respect to perturbations has not been satisfactorily answered. In this paper, we quantitatively measure this stability by considering the associated devia...

We consider perturbation of frames and frame sequences in a Hilbert space H. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of ...

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...

Given certain compactly supported functions g ∈ L2(Rd) whose Zd-translates form a partition of unity, and real invertible d×d matrices B, C for which ||CT B|| is sufficiently small, we prove that the Gabor system {EBmTCng}m,n∈Zd forms a frame, with a (non-canonical) dual Gabor frame generated by an explicitly given finite linear combination of shifts of g. For functions g of the above type and ...

In view of the good properties of nonstationary wavelet frames and the better flexibility of wavelets in Sobolev spaces, the nonstationary dual wavelet frames in a pair of dual Sobolev spaces are studied in this paper. We mainly give the oblique extension principle and the mixed extension principle for nonstationary dual wavelet frames in a pair of dual Sobolev spaces H(R) and H−s(Rd). Keywords...