Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Sbornik: Mathematics, 2016, Volume 207, Issue 3, Pages 444–457
DOI: https://doi.org/10.1070/SM8492 (Mi sm8492) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Decomposition of dyadic measures and unions of closed $\mathscr{U}$-sets for series in a Haar system

M. G. Plotnikov, Yu. A. Plotnikova

Vologda State Academy of Milk Industry
English version PDF (549 kB) Citations (6) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM8492
Abstract: New properties of finitely additive set functions (quasi-measures) and Borel measures on dyadic product groups $\mathbb{G}^m$ are established. The results obtained are applied to the theory of series in Haar systems — for example, for a broad family of classes of multiple Haar series on $\mathbb{G}^m$, a countable union of closed uniqueness sets is shown to be a uniqueness set too.
Bibliography: 18 titles.
Keywords: dyadic product group, multiple Haar series, $\mathscr{U}$-set, quasi-measure, Borel measure.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00417
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
Vologda State Dairy Farming Academy by N.V.Vereshchagin ВГМХА-2014
The research of the first-named author was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 14-01-00417) and the Programme of the President of the Russian Federation for the Support of Leading Scientific Schools (grant no. НШ-3682.2014.1). The research of the second-named author was carried out with the financial support of Vologda State Academy of Milk Industry (year 2014).
Received: 21.02.2015 and 04.07.2015
Bibliographic databases:
Document Type: Article
UDC: 517.518.113+517.518.117+517.518.36
MSC: Primary 42C25; Secondary 42A20, 42C05, 43A17
Language: English
Original paper language: Russian
Citation: M. G. Plotnikov, Yu. A. Plotnikova, “Decomposition of dyadic measures and unions of closed $\mathscr{U}$-sets for series in a Haar system”, Sb. Math., 207:3 (2016), 444–457
Citation in format AMSBIB
\Bibitem{PloPlo16}
\by M.~G.~Plotnikov, Yu.~A.~Plotnikova
\paper Decomposition of dyadic measures and unions of closed $\mathscr{U}$-sets for series in a~Haar system
\jour Sb. Math.
\yr 2016
\vol 207
\issue 3
\pages 444--457
\mathnet{http://mi.mathnet.ru//eng/sm8492}
\crossref{https://doi.org/10.1070/SM8492}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3507487}
\zmath{https://zbmath.org/?q=an:1351.42040}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2016SbMat.207..444P}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000376442700007}
\elib{https://elibrary.ru/item.asp?id=25707821}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84971264213}
Linking options:
  • https://www.mathnet.ru/eng/sm8492
  • https://doi.org/10.1070/SM8492
  • https://www.mathnet.ru/eng/sm/v207/i3/p137
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024