Department of Mathematics, Nankai University, Tianjin 300071, People's Republic of China ; Department of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
Abstract:
In this paper we give sufficient conditions for irregular Gabor systems to be frames. We show that for a large class of window functions, every relatively uniformly discrete sequence in with sufficiently high density will generate a Gabor frame. Explicit frame bounds are given. We also study the stability of irregular Gabor frames and show that every Gabor frame with arbitrary time-frequency parameters is stable if the window function is nice enough. Explicit stability bounds are given.