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arXiv · 1710.03032

Uncertainty product for Vilenkin groups

Ivan Kovalyov·Elena Lebedeva
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Abstract

We study a localization of functions defined on Vilenkin groups. To measure the localization we introduce two uncertainty products $UP_{\lambda}$ and $UP_{G}$ that are similar to the Heisenberg uncertainty product. $UP_{\lambda}$ and $UP_{G}$ differ from each other by the metric used for the Vilenkin group $G$. We discuss analogs of a quantitative uncertainty principle. Representations for $UP_{\lambda}$ and $UP_{G}$ in terms of Walsh and Haar basis are given.

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Ivan Kovalyov, Elena Lebedeva. 2017-10-09. Uncertainty product for Vilenkin groups. https://arxiv.org/abs/1710.03032

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