Simultaneous estimates for vector-valued Gabor frames of Hermite   functions
  We 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. 
Hartmut Fuehr