A Balian-Low Theorem for Subspaces

摘要

We extend the Balian-Low theorem to Gabor subspaces of L2(R) by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a lattice of rational density is a Riesz sequence generating a subspace which is invariant under an additional time-frequency shift, then its generator cannot decay fast simultaneously in time and frequency.