Abstract We extend the quantitative Balian–Low theorem of Nitzan and Olsen to higher dimensions. We use Zak transform methods and dimension reduction. The characterization of the Gabor–Riesz bases by the Zak transform allows us to reduce the problem to the quasiperiodicity and the boundedness from below of the Zak transforms of the Gabor–Riesz basis generators, two properties for which dimension reduction is possible.

中文翻译：

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更高维度的定量 Balian-Low 定理

摘要 我们将 Nitzan 和 Olsen 的定量 Balian-Low 定理扩展到更高维度。我们使用 Zak 变换方法和降维。通过 Zak 变换对 Gabor-Riesz 基的表征使我们能够将问题简化为 Gabor-Riesz 基生成器的 Zak 变换下方的准周期性和有界性，这两个属性可以降维。