This is joint work of Gerard Ascensi, Hans G. Feichtinger, and Norbert Kaiblinger.

The key result of this paper describes the fact that for an
important class of pseudodifferential operators the property of
invertibility is preserved under minor dilations of their Weyl symbols.
This observation has two implications in time-frequency analysis. First,
it implies the stability of general Gabor frames under small dilations of
its time-frequency set, previously known only for the lattice case.
Secondly, it allows us to derive a new Balian-Low theorem for Gabor
systems with window in the standard window class and with general
time-frequency families.

Supported by the Austrian Science Fund FWF grants M1149 (G.A.), P20442 (H.G.F.),
P21339 (N.K.), and the EU FET Open grant UNLocX 255931 (H.G.F.).