Multidimensional nonseparable Gabor expansions

Various generalizations of the classical Gabor expansion are considered. Studying the frame operator via the Kohn- Nirenberg correspondence allows to obtain straightforward structural results for the situation of (i) nonseparable prototypes, and/or (ii) nonseparable time-frequency sampling lattices, and/or (iii) multi-prototypes. For such general Weyl-Heisenberg frames, it is shown how to reformulate the Janssen representation of the frame operator and the Wexler- Raz result. Moreover, an analysis of the analysis operator is performed that leads to quantitative results about the variety of admissible analysis/synthesis prototypes.