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Mat. Sb., 2008, Volume 199, Number 5, Pages 3–26 (Mi msb3841)  

This article is cited in 8 scientific papers (total in 8 papers)

Non-linear approximation of continuous functions by the Faber-Schauder system

M. G. Grigoryan, A. A. Sargsyan

Yerevan State University

Abstract: The existence of a function $f_0(x)\in C_{[0,1]}$ for which the greedy algorithm in the Faber-Schauder system is divergent in measure on $[0,1]$ is established. It is shown that for each $\varepsilon$, $0<\varepsilon<1$, there exists a measurable subset $E$ of $ [0,1]$ of measure $|E|>1-\varepsilon$ such that for each $f(x)\in C_{[0,1]}$ one can find a function $\widetilde f(x)\in C_{[0,1]}$ coinciding with $f(x)$ on $E$, whose greedy algorithm in the Faber-Schauder system converges uniformly on $[0,1]$.
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DOI: https://doi.org/10.4213/sm3841

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English version:
Sbornik: Mathematics, 2008, 199:5, 629–653

Bibliographic databases:

UDC: 517.518.8+517.518.34
MSC: 42C20, 42A20
Received: 20.02.2007 and 20.02.2008

Citation: M. G. Grigoryan, A. A. Sargsyan, “Non-linear approximation of continuous functions by the Faber-Schauder system”, Mat. Sb., 199:5 (2008), 3–26; Sb. Math., 199:5 (2008), 629–653

Citation in format AMSBIB
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    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. Aleksanyan H., “On the Greedy algorithm by the Haar system”, J. Contemp. Math. Anal., 45:3 (2010), 151–161  crossref  mathscinet  zmath  isi  elib  scopus
    2. Grigoryan M.G., Sargsyan A.A., “On the coefficients of the expansion of elements from $C[0,1]$ space by the Faber-Schauder system”, J. Funct. Spaces Appl., 9:2 (2011), 191–203  crossref  mathscinet  zmath  isi  scopus
    3. M. G. Grigoryan, “Modifications of functions, Fourier coefficients and nonlinear approximation”, Sb. Math., 203:3 (2012), 351–379  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Aleksanyan H., “Nonlinear approximation by renormalized trigonometric system”, J. Contemp. Math. Anal.-Armen. Aca., 47:2 (2012), 86–96  crossref  mathscinet  zmath  isi  scopus
    5. Gogoladze L., Tsagareishvili V., “On the Divergence of Fourier Series of Functions in Several Variables”, Anal. Math., 39:3 (2013), 163–178  crossref  mathscinet  zmath  isi  scopus
    6. L. N. Galoyan, M. G. Grigoryan, A. Kh. Kobelyan, “Convergence of Fourier series in classical systems”, Sb. Math., 206:7 (2015), 941–979  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. M. G. Grigoryan, K. A. Navasardyan, “Universal functions in ‘correction’ problems guaranteeing the convergence of Fourier–Walsh series”, Izv. Math., 80:6 (2016), 1057–1083  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. M. G. Grigoryan, A. A. Sargsyan, “The Fourier–Faber–Schauder series unconditionally divergent in measure”, Siberian Math. J., 59:5 (2018), 835–842  mathnet  crossref  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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