2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76290We present a general approach to derive sampling theorems on locally compact groups from oscillation estimates. We focus on the ${\rm L}^2$-stability of the sampling operator by using notions from frame theory. This approach yields particularly simple and transparent reconstruction procedures. We then apply these methods to the discretization of discrete series representations and to Paley-Wiener spaces on stratified Lie groups.18 pagesFunctional AnalysisRepresentation TheoryPrimary 43A80, 42B35; Secondary 42C40, 26D10text