A. Caragea, D. Lee, G. E. Pfander, F. Philipp
Published 2018-01-28Version 1
We extend the Balian-Low theorem to Gabor subspaces of $L^2(\mathbb R)$ 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.
Uniform partitions of frames of exponentials into Riesz sequences
Frame set for Gabor systems with Haar window
Pointwise Convergence of Fourier Series on the Ring of Integers of Local Fields with an Application to Gabor Systems
![QR code for arXiv:1801.09237 [math.FA]](http://oss.arxitics.com/images/favicon.svg)