2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115250We derive frame estimates for vector-valued Gabor systems with window functions belonging to Schwartz space. The main result provides frame bound estimates for windows composed of Hermite functions. The proof is based on a recently established sampling theorem for the simply connected Heisenberg group, which is translated to a family of frame estimates via a direct integral decomposition.16 pagesFunctional AnalysisRepresentation Theory42C15; 42B35text