Research PaperNo Access

Uncertainty product for Vilenkin groups

Department of Mathematics, National Pedagogical Dragomanov University, Kiev, Pirogova 9, 01601, Ukraine

and

Mathematics and Mechanics Faculty, Saint Petersburg State University, Universitetskaya nab., 7-9, Saint Petersburg, 199034, Russia

St. Petersburg Polytechnical University, Department of Calculus Polytekhnicheskay, 29, 195251, St. Petersburg, Russia

E-mail Address: ealebedeva2004@gmail.com

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https://doi.org/10.1142/S0219691318500364Cited by:0 (Source: Crossref)

Abstract

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

Keywords:

AMSC: 22B99, 42C40

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