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

Abstract

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 particular, we first prove the Balian--Low theorem for arbitrary quadratic forms. Then we generalize further and prove the Balian--Low theorem for differential operators associated with a symplectic basis for the symplectic form on ${\mathbb{R}}^{2d}$.

Latex, 25 pages

Cited by in corpus (3)

• A Sharp Balian-Low Uncertainty Principle for Shift-Invariant Spaces
• Balian-Low type theorems on $L^2(\mathbb{C})$
• Wilson bases for general time-frequency lattices