The Balian--Low theorem for the symplectic form on ${\mathbb{R}}^{2d}$

John J. Benedetto, Wojciech Czaja, Andrei Ya. Maltsev

In this paper we extend the Balian--Low theorem, which is a version of the uncertainty principle for Gabor (Weyl--Heisenberg) systems, to functions of several variables. In particu…