English

A Balian-Low Theorem for Subspaces

Functional Analysis 2018-06-14 v2

Abstract

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

Cite

@article{arxiv.1801.09237,
  title  = {A Balian-Low Theorem for Subspaces},
  author = {A. Caragea and D. Lee and G. E. Pfander and F. Philipp},
  journal= {arXiv preprint arXiv:1801.09237},
  year   = {2018}
}

Comments

19 pages

R2 v1 2026-06-22T23:59:48.171Z