English

On the finite linear independence of lattice Gabor systems

Classical Analysis and ODEs 2011-09-05 v2 Functional Analysis

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(Rd)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.

Keywords

Cite

@article{arxiv.1007.2002,
  title  = {On the finite linear independence of lattice Gabor systems},
  author = {Ciprian Demeter and S. Zubin Gautam},
  journal= {arXiv preprint arXiv:1007.2002},
  year   = {2011}
}

Comments

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