Rational time-frequency multi-window subspace Gabor frames and their Gabor duals

This paper addresses the theory of multi-window subspace Gabor frame with rational time-frequency parameter products. With the help of a suitable Zak transform matrix, we characterize multi-window subspace Gabor frames, Riesz bases, orthonormal bases and the uniqueness of Gabor duals of type I and type II. Using these characterizations we obtain a class of multi-window subspace Gabor frames, Riesz bases, orthonormal bases, and at the same time we derive an explicit expression of their Gabor duals of type I and type II. As an application of the above results, we obtain characterizations of multi-window Gabor frames, Riesz bases and orthonormal bases for L-2(R), and derive a parametric expression of Gabor duals for multi-window Gabor frames in L-2(R).