Extra invariance and Balian-Low type obstructions for Gabor spaces

Kurzfassung/Abstract

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 $\varphi \in L²(\mathbb{R}^d)$.
The results are compared with the case for shift-invariant spaces where the Zak transform is replaced by Fourier transform.