RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
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


Mat. Sb., 2018, Volume 209, Number 11, Pages 32–59 (Mi msb9002)  

An abstract Kolmogorov theorem, and an application to metric spaces and topological groups

S. V. Bochkarev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Using the method of averaging over the supports of $\delta$-functions, we generalise Kolmogorov's fundamental theorem on the existence of a trigonometric Fourier series that diverges almost everywhere to any bounded biorthonormal systems of complex-valued functions on an arbitrary measurable space. The abstract Kolmogorov theorem thus obtained is applied to construct divergent Fourier series on metric spaces and topological groups. We establish the existence of a Fourier series in the system of characters of an arbitrary compact Abelian group that is divergent almost everywhere.
Bibliography: 37 titles.

Keywords: biorthonormal system, symmetrized Lebesgue functions, convergence almost everywhere, topological groups, characters.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This research was supported by the Russian Science Foundation under grant no. 14-50-00005.


DOI: https://doi.org/10.4213/sm9002

Full text: PDF file (745 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2018, 209:11, 1575–1602

Bibliographic databases:

UDC: 517.518.36+517.518.452+517.986.62
MSC: Primary 43A50; Secondary 42A50
Received: 01.08.2017 and 09.04.2018

Citation: S. V. Bochkarev, “An abstract Kolmogorov theorem, and an application to metric spaces and topological groups”, Mat. Sb., 209:11 (2018), 32–59; Sb. Math., 209:11 (2018), 1575–1602

Citation in format AMSBIB
\Bibitem{Boc18}
\by S.~V.~Bochkarev
\paper An abstract Kolmogorov theorem, and an~application to metric spaces and topological groups
\jour Mat. Sb.
\yr 2018
\vol 209
\issue 11
\pages 32--59
\mathnet{http://mi.mathnet.ru/msb9002}
\crossref{https://doi.org/10.4213/sm9002}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018SbMat.209.1575B}
\elib{http://elibrary.ru/item.asp?id=36361379}
\transl
\jour Sb. Math.
\yr 2018
\vol 209
\issue 11
\pages 1575--1602
\crossref{https://doi.org/10.1070/SM9002}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000456414300002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85062845715}


Linking options:
  • http://mi.mathnet.ru/eng/msb9002
  • https://doi.org/10.4213/sm9002
  • http://mi.mathnet.ru/eng/msb/v209/i11/p32

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    Related presentations:
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:200
    References:28
    First page:27

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019