Victoria Paternostro

Shift-modulation invariant spaces on LCA groups

Fil: Cabrelli, Carlos. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matematica; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina

Gabor fusion frames generated by difference sets

Collections of time- and frequency-shifts of suitably chosen generators (Alltop or random vectors) proved successful for many applications in sparse recovery and related fields. It is known1 that taking a characteristic function of a difference set as a generator, and considering only the frequency shifts, gives an equaingular tight frame for the subspace they span. In this paper, we investigate the system of all N2 time- and frequency-shifts of a difference set in dimension N via the mutual coherence, and compare numerically its sparse recovery effectiveness with Alltop and random generators. We further view this Gabor system as a fusion frame, show that it is optimally sparse, and moreover an equidistant tight fusion frame, i.e. it is an optimal Grassmannian packing.

Group Riesz and frame sequences: the Bracket and the Gramian

Given a discrete group and a unitary representation on a Hilbert space

Perturbations of fusion frames and the effect on their canonical dual

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The Zak transform and the structure of spaces invariant by the action of an LCA group

H, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of

Extra invariance of shift-invariant spaces on LCA groups

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