Extra invariance and Balian-Low type obstructions for Gabor spaces

CABRELLI, CARLOS A.; LEE, DAE GWAN; MOLTER, URSULA M.; PFANDER, GOETZ

Tallin

Congreso; 12th International Conference on Sampling Theory and Applications, SampTA 2017; 2017

SAMPTA

We establish some Balian-Low type results for Gabor spaces, which concern with discontinuity in some periodization of $Z \varphi$, where $Z \varphi$ is the Zak transform of the window function $\varphi \in L^2(\mathbb{R}^d)$.The results are compared with the case for shift-invariant spaces where the Zak transform is replaced by Fourier transform.