On the finite linear independence of lattice Gabor systems

Details On the finite linear independence of lattice Gabor systems On the finite linear independence of lattice Gabor systems

2010-07-12

arxiv.org/abs/1007.2002v2

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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 $L^2(\mathbb R^d)$. Our proof is based on a simple argument from the spectral theory of random Schr\"odinger operators; in the one-dimensional setting, we recover the full strength of Linnell's result for general lattices.

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