RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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. (N.S.), 1973, Volume 91(133), Number 1(5), Pages 134–141 (Mi msb3108)  

This article is cited in 1 scientific paper (total in 1 paper)

An example of an orthonormal system of convergence in $C$ but not in $L^2$

A. M. Olevskii


Abstract: We prove the following theorem.
Theorem. {\it For any $p_0\in[1,\infty)$ there exists a complete uniformly bounded orthonormal system $\{\varphi_n\}$ having the following properties}:
1) For all $f\in L^p, p>p_0,$ the Fouries series $\sum c_n\varphi_n$ converges to $f$ almost everywhere.
2) {\it There exists an $F\in L^{p_0}$ whose Fourier series diverges almost everywhere.}
Bibliography: 8 titles.

Full text: PDF file (666 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1973, 20:1, 145–153

Bibliographic databases:

UDC: 517.522.3
MSC: Primary 42A20; Secondary 42A60, 42A64
Received: 03.10.1972

Citation: A. M. Olevskii, “An example of an orthonormal system of convergence in $C$ but not in $L^2$”, Mat. Sb. (N.S.), 91(133):1(5) (1973), 134–141; Math. USSR-Sb., 20:1 (1973), 145–153

Citation in format AMSBIB
\Bibitem{Ole73}
\by A.~M.~Olevskii
\paper An~example of an orthonormal system of convergence in~$C$ but not in~$L^2$
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 91(133)
\issue 1(5)
\pages 134--141
\mathnet{http://mi.mathnet.ru/msb3108}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=333574}
\zmath{https://zbmath.org/?q=an:0274.42014}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 20
\issue 1
\pages 145--153
\crossref{https://doi.org/10.1070/SM1973v020n01ABEH001863}


Linking options:
  • http://mi.mathnet.ru/eng/msb3108
  • http://mi.mathnet.ru/eng/msb/v133/i1/p134

    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

    This publication is cited in the following articles:
    1. A. S. Krantsberg, “On divergent Fourier series in orthogonal systems”, Math. USSR-Sb., 22:4 (1974), 547–560  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:267
    Full text:88
    References:32

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