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

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

2002-12-13

arxiv.org/abs/math/0212186v1

Journ. of Math. Phys. 44:4, 1735-1750 (2003)

Mathematics

Functional Analysis

Latex, 25 pages

Scientific paper

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 ${\mathbb R}^{2d}$.

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