Characterizations of Gabor systems via the Fourier transform (Q1585382)

Consider a set of functions \(g^1,...,g^L \in L^2(R^d)\). Given nondegenerate \(d \times d\) matrices \(A,B\), the associated Gabor system is the set of functions \(\{e^{2\pi i Am \cdot x} g^k(x- Bn) \}_{m,n \in Z^d, k=1,..,L}\). The paper gives (in terms of the Fourier transform) equivalent conditions for the Gabor system to be an orthogonal system in \(L^2(R^d)\) or a tight frame.