Simultaneous estimates for vector-valued Gabor frames of Hermite functions (Q960006)

The aim of this paper is to derive frame estimates for vector-valued Gabor systems. These in the space of vector-valued signals are obtained by picking a window function, and applying translations and modulations. The main result provides estimates for windows composed of Heimite 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 bound estimates via a direct integral decomposition.