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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 5, Pages 1057–1065
DOI: https://doi.org/10.17377/smzh.2018.59.508
(Mi smj3028)
 

This article is cited in 2 scientific papers (total in 2 papers)

The Fourier–Faber–Schauder series unconditionally divergent in measure

M. G. Grigoryana, A. A. Sargsyanb

a Yerevan State University, Yerevan, Armenia
b Russian-Armenian University, Yerevan, Armenia
Full-text PDF (294 kB) Citations (2)
References:
Abstract: We prove that, for every $\varepsilon\in (0,1)$, there is a measurable set $E\subset[0,1]$ whose measure $|E|$ satisfies the estimate $|E|>1-\varepsilon$ and, for every function $f\in C_{[0,1]}$, there is $\tilde f\in C_{[0,1]}$ coinciding with $f$ on $E$ whose expansion n the Faber–Schauder system diverges in measure after a rearrangement.
Keywords: uniform convergence, Faber–Schauder system, convergence in measure.
Received: 11.12.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 5, Pages 835–842
DOI: https://doi.org/10.1134/S0037446618050087
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: M. G. Grigoryan, A. A. Sargsyan, “The Fourier–Faber–Schauder series unconditionally divergent in measure”, Sibirsk. Mat. Zh., 59:5 (2018), 1057–1065; Siberian Math. J., 59:5 (2018), 835–842
Citation in format AMSBIB
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\paper The Fourier--Faber--Schauder series unconditionally divergent in measure
\jour Sibirsk. Mat. Zh.
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\vol 59
\issue 5
\pages 1057--1065
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\crossref{https://doi.org/10.17377/smzh.2018.59.508}
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\transl
\jour Siberian Math. J.
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\issue 5
\pages 835--842
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  • https://www.mathnet.ru/eng/smj/v59/i5/p1057
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Full-text PDF :54
    References:43
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