On perturbations of irregular Gabor frames

We give a new sufficient condition under which an irregular Gabor system {e^2πipλxψ(x-q_λ)} forms a Bessel sequence for L²(ℝ). The Bessel bound just requires a mild decay on ψ. This condition then can be used to prove stability of an irregular Gabor frame under a perturbation of its generating function. We go on to outline how the perturbation result can be used to extend a sufficient condition of Heller for irregular Gabor frames with compactly supported generator to the case of a noncompactly supported generator.