By Mads Sielemann Jakobsen, Jakob Lemvig
We examine Gabor frames on in the neighborhood compact abelian teams with time–frequency shifts alongside non-separable, closed subgroups of the part house. Density theorems in Gabor research country helpful stipulations for a Gabor procedure to be a body or a Riesz foundation, formulated in basic terms when it comes to the index subgroup. within the classical effects the subgroup is believed to be discrete. We turn out density theorems for normal closed subgroups of the section area, 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 platforms with time–frequency shifts alongside non-separable, closed subgroups of the section area. Even within the euclidean surroundings, our effects are new.
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Additional info for Density and duality theorems for regular Gabor frames
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