Perturbation of frames and applications to Gabor frames

We prove a stability result for frames, with a perturbation condition that generalizes the Paley-Wiener condition used in the context of bases. We show how the result can be applied to different types of perturbations of a Gabor frame {e imbx f(x — na)} m,n∈ℤ of L 2(ℝ), e.g., perturbation of f or na.