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

John J. Benedetto·Wojciech Czaja·Andrei Ya. Maltsev
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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 ${\mathbb R}^{2d}$.

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John J. Benedetto, Wojciech Czaja, Andrei Ya. Maltsev. 2002-12-13. The Balian--Low theorem for the symplectic form on ${\mathbb R}^{2d}$. https://doi.org/10.1063/1.1559415

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