Gabor orthonormal bases, tiling and periodicity

Alberto Debernardi Pinos, Nir Lev

We show that if the Gabor system $\{g(x-t)e^{2\pi isx}\}$, $t\in T$, $s\in S$, is an orthonormal basis in $L^2(\mathbb{R})$ and if the window function $g$ is compactly supported…