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Arati, S.; Devaraj, P.

On Riesz duals for Gabor systems on LCA groups. (English) Zbl 07905934

Rend. Circ. Mat. Palermo (2) 73, No. 5, 1801-1815 (2024).
Summary: In the context of separable uniform time-frequency lattices in locally compact abelian groups, we analyse the circumstances in which, for a given Gabor frame, the adjoint Gabor system is an R-dual of the Gabor frame. In this regard, we also prove a necessary condition for a given Gabor Bessel sequence to be complete.

MSC:

42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
43A70 Analysis on specific locally compact and other abelian groups
43A32 Other transforms and operators of Fourier type

Keywords:

adjoint Gabor systems; completeness; frames; Gabor systems; LCA groups; R-duals
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Full Text: DOI arXiv

References:

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