On the finite linear independence of lattice Gabor systems

2010/07/12 by Ciprian Demeter, Demeter, Ciprian, S. Zubin Gautam +1 · 1 citation
Mathematics · #26B99 #42B99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 42C40 #Secondary 46B15 #math.CA #math.FA #msc:26B99 #msc:42B99 #msc:42C40 #msc:46B15

paper · pdf · doi:10.48550/arxiv.1007.2002

13 pages, no figures. Minor errors corrected, additional explanation added to proofs in Section 4

arxiv created 2011/09/02 · arxiv updated 2011/09/05

Abstract

In the restricted setting of product phase space lattices, we give an alternate proof of P. Linnell's theorem on the finite linear independence of lattice Gabor systems in L²(\mathbb R^d). Our proof is based on a simple argument from the spectral theory of random Schrödinger operators; in the one-dimensional setting, we recover the full strength of Linnell's result for general lattices.

Cited by

• Linear independence of time-frequency translates for ultimately positive functions

Related

• Gabor frames in ℓ²(\mathbf Z) and linear dependence
• Trichotomy for the HRT Conjecture for mixed integer configuration
• On the structure of multivariate Gabor systems and a result on Gaussian Gabor frames
• On Riesz duals for the Gabor system on LCA groups
• On the Parity under Metapletic Operators and an Extension of a Result of\n Lyubarskii and Nes