Balian-Low Theorems in Several Variables

DOI10.1007/978-3-030-57464-2_10arXiv1807.03856MaRDI QIDQ6304067

Josiah Park, Michael V. Northington

Publication date: 10 July 2018

Abstract: Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for discrete Gabor systems defined on $mathbb{Z}_d$. Here we extend these results to a multivariable setting. Additionally, we show a variety of applications of the Quantitative BLT, proving in particular nonsymmetric BLTs in both the discrete and continuous setting for functions with more than one argument. Finally, in direct analogy of the continuous setting, we show the Quantitative Finite BLT implies the Finite BLT.

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15)

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