On Riesz duals for the Gabor system on LCA groups

TL;DR

This paper investigates the conditions under which the adjoint Gabor system acts as an R-dual of a Gabor frame on locally compact abelian groups, providing insights into duality and completeness in this mathematical context.

Contribution

It introduces new criteria for R-duals of Gabor frames and establishes a necessary condition for Gabor Bessel sequences to be complete in LCA groups.

Findings

Characterization of R-duals for Gabor systems on LCA groups

Necessary condition for Gabor Bessel sequences to be complete

Analysis of duality in the context of uniform time-frequency lattices

Abstract

In this paper, we analyse the circumstances in which the adjoint Gabor system is an R-dual of a given Gabor frame in the context of separable uniform time-frequency lattices in locally compact abelian groups. In this regard, we also prove a necessary condition for a Gabor Bessel sequence in this setting to be complete.