Uncertainty product for Vilenkin groups-Reference-Cited by-同舟云学术

Uncertainty product for Vilenkin groups

Published:2018-09 Issue:05 Volume:16 Page:1850036
ISSN:0219-6913
Container-title:International Journal of Wavelets, Multiresolution and Information Processing
language:en
Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.

Author:

Kovalyov Ivan¹,Lebedeva Elena²³^ORCID

Affiliation:

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

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

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

Abstract

We study a localization of functions defined on Vilenkin groups. To measure the localization, we introduce two uncertainty products [Formula: see text] and [Formula: see text] that are similar to the Heisenberg uncertainty product. [Formula: see text] and [Formula: see text] differ from each other by the metric used for the Vilenkin group [Formula: see text]. We discuss analogs of a quantitative uncertainty principle. Representations for [Formula: see text] and [Formula: see text] in terms of Walsh and Haar basis are given.

Funder

Volkswagen Foundation

Russian Foundation for Basic Research

Saint Petersburg State University

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Information Systems,Signal Processing

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219691318500364

Reference13 articles.

1. Uncertainty measures and uncertainty relations for angle observables

2. Uncertainty principles on compact Riemannian manifolds

3. Multiresolution analysis and wavelets on Vilenkin groups

4. Walsh Series and Transforms