arXiv math/02121862002-12-13math.FA

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

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

备注：: Latex, 25 pages
发表信息：: Journ. of Math. Phys. 44:4, 1735-1750 (2003)
DOI：: 10.1063/1.1559415

英文摘要：

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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