@article{cabrelli-molter-pfander,
title = "Time–frequency shift invariance and the Amalgam Balian–Low theorem ",
journal = "Applied and Computational Harmonic Analysis ",
volume = "",
number = "0",
pages = " - ",
year = "2015",
note = "",
issn = "1063-5203",
doi = "http://dx.doi.org/10.1016/j.acha.2015.04.003",
url = "http://www.sciencedirect.com/science/article/pii/S1063520315000524",
author = "Carlos Cabrelli and Ursula Molter and Götz E. Pfander",
keywords = "Balian–Low theorem",
keywords = "Additional shift invariance",
keywords = "Gabor frames",
keywords = "Time–frequency analysis",
keywords = "Feichtinger algebra ",
abstract = "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. "
}