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. (N.S.), 1976, Volume 99(141), Number 3, Pages 356–365 (Mi msb2755)  

This article is cited in 17 scientific papers (total in 17 papers)

On a complete orthonormal system

B. S. Kashin


Abstract: In this paper we construct in $L_2(0,1)$ a complete orthonormal system $\{\psi_n(x)\}_{n=1}^\infty$ for which every series $\sum_{n=1}^\infty c_n\psi_n(x)$ whose coefficients satisfy the condition $\sum_{n=1}^\infty c_n^2=\infty$ diverges on a set of positive measure.
Bibliography: 6 titles.

Full text: PDF file (670 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1976, 28:3, 315–324

Bibliographic databases:

UDC: 517.52
MSC: 40A05, 42A56
Received: 20.05.1975

Citation: B. S. Kashin, “On a complete orthonormal system”, Mat. Sb. (N.S.), 99(141):3 (1976), 356–365; Math. USSR-Sb., 28:3 (1976), 315–324

Citation in format AMSBIB
\Bibitem{Kas76}
\by B.~S.~Kashin
\paper On a~complete orthonormal system
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 99(141)
\issue 3
\pages 356--365
\mathnet{http://mi.mathnet.ru/msb2755}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=410248}
\zmath{https://zbmath.org/?q=an:0338.42016}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 3
\pages 315--324
\crossref{https://doi.org/10.1070/SM1976v028n03ABEH001654}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976EM69200004}


Linking options:
  • http://mi.mathnet.ru/eng/msb2755
  • http://mi.mathnet.ru/eng/msb/v141/i3/p356

    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. Kashin B., “Orthogonal Convergence Systems”, 228, no. 2, 1976, 285–286  mathscinet  zmath  isi
    2. Ivanov V., “the Coefficients of the Orthogonal Universal Series and Zero-Series”, 272, no. 1, 1983, 19–23  mathscinet  zmath  isi
    3. M. G. Grigoryan, “On convergence of Fourier series in complete orthonormal systems in the $L^1$-metric and almost everywhere”, Math. USSR-Sb., 70:2 (1991), 445–466  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. A. Talalyan, R. I. Ovsepian, “The representation theorems of D. E. Men'shov and their impact on the development of the metric theory of functions”, Russian Math. Surveys, 47:5 (1992), 13–47  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. P. L. Ul'yanov, “Development of D. E. Men'shov's results in the theory of orthogonal series”, Russian Math. Surveys, 47:5 (1992), 49–70  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Ulyanov P., “Menshoff,D.Y. Papers on the Theory of Orthogonal Series and its Further Development”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1992, no. 4, 8–24  mathscinet  isi
    7. M. G. Grigoryan, “On some properties of orthogonal systems”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 261–289  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. Szabo V., “a Note to a Theorem of Talaljan”, Acta Math. Hung., 73:4 (1996), 263–275  crossref  mathscinet  zmath  isi
    9. Kozma G. Olevskii A., “Menshov Representation Spectra”, J. Anal. Math., 84 (2001), 361–393  crossref  mathscinet  zmath  isi
    10. M. G. Grigoryan, “On an orthonormal system”, Russian Math. (Iz. VUZ), 46:4 (2002), 22–26  mathnet  mathscinet  zmath  elib
    11. M. G. Grigoryan, “On the $L^p_\mu$-strong property of orthonormal systems”, Sb. Math., 194:10 (2003), 1503–1532  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. Kazarian K., “A complete orthonormal system of divergence”, C. R. Math. Acad. Sci. Paris, 337:2 (2003), 85–88  crossref  mathscinet  zmath  isi
    13. A. M. Olevskii, “Representation of functions by exponentials with positive frequencies”, Russian Math. Surveys, 59:1 (2004), 171–180  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. Kazarian K., “The zero-one law for a complete orthonormal system”, C. R. Math. Acad. Sci. Paris, 339:5 (2004), 335–337  crossref  mathscinet  zmath  isi
    15. Kazarian K.S., “A complete orthonormal system of divergence”, J. Funct. Anal., 214:2 (2004), 284–311  crossref  mathscinet  zmath  isi
    16. K. S. Kazarian, “On the Ul'yanov problem”, Sb. Math., 197:12 (2006), 1805–1826  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. Sh. T. Tetunashvili, “Universal series and subsequences of functions”, Sb. Math., 209:10 (2018), 1498–1532  mathnet  crossref  crossref  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:418
    Full text:115
    References:37
    First page:2

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