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. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 1972, Volume 12, Issue 5, Pages 511–516 (Mi mz9910)  

The absolute convergence of orthogonal series

A. S. Zinov'ev

Khar'kov Aviation Institute

Abstract: We obtain sufficient conditions for the absolute convergence of Fourier series for functions of $\mathrm{L}^2_{\mathrm{d}\psi}$ depending on the properties of the function being expanded and the rate of growth of the sums $\sum_{k=1}^n\varphi_k^2(x)$ of the system of functions $\{\varphi_k(\mathrm{t})\}$ orthonormalized in $[a,\mathrm{ b}]$ with respect to $\mathrm{d}\psi(\mathrm{t})$. We show that if at some point $x\in[a,\mathrm{b}]$ the function $\psi(\mathrm{t})$ has a discontinuity, at that point the Fourier series of any function $f(\mathrm{t})\in \mathrm{L}_{\mathrm{d}\psi}^2$, converges absolutely.

Full text: PDF file (519 kB)

English version:
Mathematical Notes, 1972, 12:5, 743–746

Bibliographic databases:

UDC: 517.5
Received: 31.01.1972

Citation: A. S. Zinov'ev, “The absolute convergence of orthogonal series”, Mat. Zametki, 12:5 (1972), 511–516; Math. Notes, 12:5 (1972), 743–746

Citation in format AMSBIB
\Bibitem{Zin72}
\by A.~S.~Zinov'ev
\paper The absolute convergence of orthogonal series
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 5
\pages 511--516
\mathnet{http://mi.mathnet.ru/mz9910}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=318766}
\zmath{https://zbmath.org/?q=an:0271.42010}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 5
\pages 743--746
\crossref{https://doi.org/10.1007/BF01099056}


Linking options:
  • http://mi.mathnet.ru/eng/mz9910
  • http://mi.mathnet.ru/eng/mz/v12/i5/p511

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:63
    Full text:27
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020