2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70019The paper studies weak Paley-Wiener properties for group extensions by use of Mackey's theory. The main theorem establishes sufficient conditions on the dual action to ensure that the group has the weak Paley-Wiener property. The theorem applies to yield the weak Paley-Wiener property for large classes of simply connected, connected solvable Lie groups (including exponential Lie groups), but also criteria for non-unimodular groups or motion groups.22 pagesFunctional AnalysisRepresentation Theory43A30;22E27text