Shift-generated dual frames on a class of nilpotent Lie groups

Abstract

Let G be a connected, simply connected nilpotent Lie group whose irreducible unitary representations are square-integrable modulo the center. We obtain characterization results for oblique duals associated with shift-generated systems in L2(G). As a consequence of our results for the Heisenberg group, a reproducing formula associated with the orthonormal Gabor systems of L2(Rd) is obtained. © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2026.