A Quantitative Balian-Low Theorem for Higher Dimensions

Abstract

We extend the quantitative Balian-Low theorem of Nitzan and Olsen to higher dimensions. We use Zak transform methods and dimension reduction. The characterization of the Gabor-Riesz bases by the Zak transform allows us to reduce the problem to the quasiperiodicity and the boundedness from below of the Zak transforms of the Gabor-Riesz basis generators, two properties for which dimension reduction is possible. © 2018 Walter de Gruyter GmbH, Berlin/Boston 2018.