Time-frequency shift invariance and the Amalgan Balian Low Theorem

CARLOS CABRELLI; URSULA MOLTER; GÖTZ E. PFANDER

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2016 vol. 41 p. 677 - 691

1063-5203

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