  We look at the time-frequency localisation of generators of lattice Gabor
systems. For a generator of a Riesz basis, this localisation is described by
the classical Balian-Low theorem. We establish Balian-Low type theorems for
complete and minimal Gabor systems with a frame-type approximation property.
These results describe how the best possible localisation of a generator is
limited by the degree of control over the coefficients in approximations given
by the system, and provide a continuous transition between the classical
Balian-Low conditions and the corresponding conditions for generators of
complete and minimal systems. Moreover, this holds for the non-symmetric
generalisations of these theorems as well.
