The Balian--Low theorem for the symplectic form on ${\mathbb R}^{2d}$
Functional Analysis
2015-06-26 v1
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 .
Cite
@article{arxiv.math/0212186,
title = {The Balian--Low theorem for the symplectic form on ${\mathbb R}^{2d}$},
author = {John J. Benedetto and Wojciech Czaja and Andrei Ya. Maltsev},
journal= {arXiv preprint arXiv:math/0212186},
year = {2015}
}
Comments
Latex, 25 pages