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, 2017, Volume 208, Issue 4, Pages 510–530
DOI: https://doi.org/10.1070/SM8643 (Mi sm8643) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Rotation of coordinate system and differentiation of integrals with respect to translation-invariant bases

G. G. Oniani, K. A. Chubinidze

Akaki Tsereteli State University, Kutaisi, Georgia
English version PDF (565 kB) Citations (6)
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM8643
Abstract: We study the dependence of differential properties of the indefinite integral on the rotation of the coordinate system (that is, on the transformation (of the variables) that is a rotation about the origin); in particular, we study Zygmund's problem concerning the possibility of correcting an arbitrary integrable function using a rotation to achieve the differentiability of its integral for general differential bases, and also the problem of invariance for the differentiability property of the integral with respect to rotations. The results obtained in the paper imply negative solutions of the above questions for bases of rather general form.
Bibliography: 19 titles.
Keywords: differentiation basis, translation-invariant basis, integral, rotation, coordinate system.
Funding agency Grant number
Shota Rustaveli National Science Foundation 31/48
The research of G. G. Oniani was supported by the Shota Rustaveli National Science Foundation (grant no. 31/48).
Received: 04.12.2015 and 05.12.2016
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 4, Pages 51–72
DOI: https://doi.org/10.4213/sm8643
Bibliographic databases:
Document Type: Article
UDC: 517.518
MSC: 28A15
Language: English
Original paper language: Russian
Citation: G. G. Oniani, K. A. Chubinidze, “Rotation of coordinate system and differentiation of integrals with respect to translation-invariant bases”, Mat. Sb., 208:4 (2017), 51–72; Sb. Math., 208:4 (2017), 510–530
Citation in format AMSBIB
\Bibitem{OniChu17}
\by G.~G.~Oniani, K.~A.~Chubinidze
\paper Rotation of coordinate system and differentiation of integrals with respect to translation-invariant bases
\jour Mat. Sb.
\yr 2017
\vol 208
\issue 4
\pages 51--72
\mathnet{http://mi.mathnet.ru/sm8643}
\crossref{https://doi.org/10.4213/sm8643}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3629083}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2017SbMat.208..510O}
\elib{https://elibrary.ru/item.asp?id=28931464}
\transl
\jour Sb. Math.
\yr 2017
\vol 208
\issue 4
\pages 510--530
\crossref{https://doi.org/10.1070/SM8643}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000405685300003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85021149740}
Linking options:
  • https://www.mathnet.ru/eng/sm8643
  • https://doi.org/10.1070/SM8643
  • https://www.mathnet.ru/eng/sm/v208/i4/p51
    • 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
    Statistics & downloads:
    Abstract page:524
    Russian version PDF:99
    English version PDF:9
    References:53
    First page:28
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024