The Balian-Low theorem for the symplectic form on R2d
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 ${\mathbb R}^{2d}$.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- April 2003
- DOI:
- 10.1063/1.1559415
- arXiv:
- arXiv:math/0212186
- Bibcode:
- 2003JMP....44.1735B
- Keywords:
-
- 03.65.Ca;
- Formalism;
- Mathematics - Functional Analysis
- E-Print:
- Latex, 25 pages