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Mat. Zametki, 1972, Volume 11, Issue 5, Pages 499–508 (Mi mz9816)  

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

On the convergence of orthogonal series to $+\infty$

R. I. Ovsepyan

Mathematics and Mechanics Institute, Academy of Sciences of the Armenian SSR

Abstract: For any sequence of numbers $a_n\downarrow0$, $\sum_{n=1}^\infty a_n^2=\infty$, a uniformly bounded orthonormal system of continuous functions $\varphi_n(x)$ which is complete in $L_2(0,1)$, and a sequence of numbers $b_n$ ($0<b_n\leqslant a_n$) are constructed such that $\sum_{n=1}^\infty b_n\varphi_n(x)=\infty$ everywhere on $(0, 1)$.

Full text: PDF file (975 kB)

English version:
Mathematical Notes, 1972, 11:5, 305–310

Bibliographic databases:

UDC: 517.5
Received: 07.06.1971

Citation: R. I. Ovsepyan, “On the convergence of orthogonal series to $+\infty$”, Mat. Zametki, 11:5 (1972), 499–508; Math. Notes, 11:5 (1972), 305–310

Citation in format AMSBIB
\Bibitem{Ovs72}
\by R.~I.~Ovsepyan
\paper On the convergence of orthogonal series to $+\infty$
\jour Mat. Zametki
\yr 1972
\vol 11
\issue 5
\pages 499--508
\mathnet{http://mi.mathnet.ru/mz9816}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=306803}
\zmath{https://zbmath.org/?q=an:0246.42010|0243.42021}
\transl
\jour Math. Notes
\yr 1972
\vol 11
\issue 5
\pages 305--310
\crossref{https://doi.org/10.1007/BF01158642}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
  • Математические заметки Mathematical Notes
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