Uncertainty product for Vilenkin groups

2017/10/09 by Kovalyov, Ivan, Lebedeva, Elena
#22B99 #42C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.03032

Abstract

We study a localization of functions defined on Vilenkin groups. To measure the localization we introduce two uncertainty products UP_λ and UP_G that are similar to the Heisenberg uncertainty product. UP_λ 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_λ and UP_G in terms of Walsh and Haar basis are given.

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