  Functional Gabor single-frame or multi-frame generator multipliers are the
matrices of function entries that preserve Parseval Gabor single-frame or
multi-frame generators. An interesting and natural question is how to
characterize all such multipliers. This question has been answered for several
special cases including the case of single-frame generators in two dimensions
and the case of multi-frame generators in one-dimension. In this paper we
completely characterize multipliers for Gabor single-frame and multi-frame
generators with respect to separable time-frequency lattices in any given
dimension. Our approach is general and applies to the previously known cases as
well.
