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

This article is cited in 18 scientific papers (total in 18 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.

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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
\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
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 3
\pages 315--324

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    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  mathscinet  adsnasa  isi  elib
    18. Kholshchevnikova N., “The Union Problem and the Category Problem of Sets of Uniqueness in the Theory of Orthogonal Series”, Real Anal. Exch., 44:1 (2019), 65–76  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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