Extra Invariance and the Amalgam Balian-Low Theorem

URSULA M. MOLTER

Barranquilla

Congreso; V Congreso Latinoamericano de Matematica; 2016

UMALCA

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.