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 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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Luef, Wiener amalgam spaces for the fundamental identity of Gabor analysis, Collect. Math. Extra (2006) 233–253. G. Feichtinger, G. Zimmermann, A Banach space of test functions for Gabor analysis, in: Gabor Analysis and Algorithms, in: Applied and Numerical Harmonic Analysis, Birkhäuser Boston, Boston, MA, 1998, pp. 123–170. H. Fremlin, Measure Theory. Vol. 4: Topological Measure Spaces, Torres Fremlin, Colchester, 2006. S. Jakobsen, J. -P. Gabardo, D. Han, Frames associated with measurable spaces, Adv.
Ross, Abstract Harmonic Analysis. Vol. I: Structure of Topological Groups. Integration Theory, Group Representations, second edition, Die Grundlehren der Mathematischen Wissenschaften, vol. 115, Springer-Verlag, Berlin–New York, 1963.  E. A. Ross, Abstract Harmonic Analysis. Vol. II: Structure and Analysis for Compact Groups. Analysis on Locally Compact Abelian Groups, Die Grundlehren der Mathematischen Wissenschaften, vol. 152, Springer-Verlag, New York, 1970. S. Jakobsen, J. Lemvig, Reproducing formulas for generalized translation invariant systems on locally compact abelian groups, Trans.
Boston, MA, 1994.  J. Ramanathan, T. Steger, Incompleteness of sparse coherent states, Appl. Comput. Harmon. Anal. 2 (2) (1995) 148–153. A. Rieﬀel, Projective modules over higher-dimensional noncommutative tori, Canad. J. Math. 40 (2) (1988) 257–338.  A. Ron, Z. Shen, Weyl–Heisenberg frames and Riesz bases in L2 (Rd ), Duke Math. J. 89 (2) (1997) 237–282. T. Stoeva, O. Christensen, On R-duals and the duality principle in Gabor analysis, J. Fourier Anal. Appl. 21 (2) (2015) 383–400. -Q.