{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T15:06:36Z","timestamp":1758121596296,"version":"3.37.3"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100001663","name":"Volkswagen Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001663","name":"Volkswagen Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["15-01-05796"],"award-info":[{"award-number":["15-01-05796"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004285","name":"Saint Petersburg State University","doi-asserted-by":"publisher","award":["9.38.198.2015"],"award-info":[{"award-number":["9.38.198.2015"]}],"id":[{"id":"10.13039\/501100004285","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2018,9]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s0219691318500364","type":"journal-article","created":{"date-parts":[[2018,4,9]],"date-time":"2018-04-09T03:10:54Z","timestamp":1523243454000},"page":"1850036","source":"Crossref","is-referenced-by-count":1,"title":["Uncertainty product for Vilenkin groups"],"prefix":"10.1142","volume":"16","author":[{"given":"Ivan","family":"Kovalyov","sequence":"first","affiliation":[{"name":"Department of Mathematics, National Pedagogical Dragomanov University, Kiev, Pirogova 9, 01601, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9054-7074","authenticated-orcid":false,"given":"Elena","family":"Lebedeva","sequence":"additional","affiliation":[{"name":"Mathematics and Mechanics Faculty, Saint Petersburg State University, Universitetskaya nab., 7-9, Saint Petersburg, 199034, Russia"},{"name":"St. Petersburg Polytechnical University, Department of Calculus Polytekhnicheskay, 29, 195251, St. Petersburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,9,11]]},"reference":[{"key":"S0219691318500364BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF00737323"},{"key":"S0219691318500364BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2009.08.012"},{"key":"S0219691318500364BIB003","doi-asserted-by":"publisher","DOI":"10.2298\/FUEE0803309F"},{"volume-title":"Elements of Dyadic Analysis","year":"2007","author":"Golubov B. I.","key":"S0219691318500364BIB004"},{"key":"S0219691318500364BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3288-6"},{"key":"S0219691318500364BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01397280"},{"volume-title":"Abstract Harmonic Analysis","year":"1970","author":"Hewitt E.","key":"S0219691318500364BIB007"},{"key":"S0219691318500364BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2014.10.043"},{"key":"S0219691318500364BIB009","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141093248049"},{"key":"S0219691318500364BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2015.05.005"},{"key":"S0219691318500364BIB011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1988-0946433-5"},{"volume-title":"Walsh Series. An Introduction to Dyadic Harmonic Analysis","year":"1990","author":"Schipp F.","key":"S0219691318500364BIB012"},{"key":"S0219691318500364BIB013","first-page":"296","author":"Schr\u00f6dinger E.","year":"1930","journal-title":"Proc. Prussian Acad. Sci."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691318500364","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,23]],"date-time":"2019-09-23T17:40:29Z","timestamp":1569260429000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691318500364"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9]]},"references-count":13,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2018,9,11]]},"published-print":{"date-parts":[[2018,9]]}},"alternative-id":["10.1142\/S0219691318500364"],"URL":"https:\/\/doi.org\/10.1142\/s0219691318500364","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2018,9]]}}}