By Mads Sielemann Jakobsen, Jakob Lemvig
http://www.sciencedirect.com/science/article/pii/S0022123615004152
We examine Gabor frames on in the neighborhood compact abelian teams with time–frequency shifts alongside non-separable, closed subgroups of the section area. Density theorems in Gabor research nation valuable stipulations for a Gabor approach to be a body or a Riesz foundation, formulated simply by way of the index subgroup. within the classical effects the subgroup is believed to be discrete. We turn out density theorems for common closed subgroups of the part house, the place the mandatory stipulations are given by way of the “size” of the subgroup. From those density effects we can expand the classical Wexler–Raz biorthogonal relatives and the duality precept in Gabor research to Gabor structures with time–frequency shifts alongside non-separable, closed subgroups of the section area. Even within the euclidean environment, our effects are new.
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