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Mathematics of the USSR-Sbornik, 1973, Volume 20, Issue 1, Pages 145–153
DOI: https://doi.org/10.1070/SM1973v020n01ABEH001863
(Mi sm3108)
 

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
References:
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.
Received: 03.10.1972
Bibliographic databases:
UDC: 517.522.3
MSC: Primary 42A20; Secondary 42A60, 42A64
Language: English
Original paper language: Russian
Citation: A. M. Olevskii, “An example of an orthonormal system of convergence in $C$ but not in $L^2$”, 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 Math. USSR-Sb.
\yr 1973
\vol 20
\issue 1
\pages 145--153
\mathnet{http://mi.mathnet.ru//eng/sm3108}
\crossref{https://doi.org/10.1070/SM1973v020n01ABEH001863}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=333574}
\zmath{https://zbmath.org/?q=an:0274.42014}
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  • https://doi.org/10.1070/SM1973v020n01ABEH001863
  • https://www.mathnet.ru/eng/sm/v133/i1/p134
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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