Time-Frequency Shift Invariance of Gabor Spaces

We consider non-complete Gabor frame sequences generated by an S 0 -function and a lattice Λ and prove that there is m ∈ ℕ such that all time-frequency shifts leaving the corresponding Gabor space invariant have their parameters in $\frac{1}{m}\Lambda $. We also investigate time-frequency shift invariance under duality aspects.