Time-frequency shift invariance and the Amalgan Balian Low Theorem
Classical Analysis and ODEs
2014-10-28 v1
Abstract
We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation-modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linear span, a Gabor space, has any additional translation-modulation invariance, then its generator cannot decay well in time and in frequency simultaneously.
Keywords
Cite
@article{arxiv.1410.7085,
title = {Time-frequency shift invariance and the Amalgan Balian Low Theorem},
author = {Carlos Cabrelli and Ursula Molter and Götz E. Pfander},
journal= {arXiv preprint arXiv:1410.7085},
year = {2014}
}
Comments
16 pages, 1 figure