A Balian-Low Theorem for Subspaces

2018/01/28 by A. Caragea, Caragea, A., D. Lee +5
Mathematics · #30H35 #42C15 #42C30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:30H35 #msc:42C15 #msc:42C30

paper · pdf · doi:10.48550/arxiv.1801.09237

19 pages

arxiv created 2018/06/13 · arxiv updated 2018/06/14

Abstract

We extend the Balian-Low theorem to Gabor subspaces of L²(\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.

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