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Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 2, Pages 30–39 (Mi ivm8772)  

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

Nonlinear approximation of functions from the class $L^r$ with respect to the Vilenkin system

M. G. Grigoryan, S. A. Sargsyan

Chair of Higher Mathematics, Erevan State University, Erevan, Republic of Armeniya

Abstract: In this paper we prove that for any function $f$ from the class $L^r$ on $[0,1)$ one can find a function $g$ from the same class (which differs from $f$ on a set of arbitrarily small measure) whose greedy algorithm with respect to the Vilenkin system converges to $f$.

Keywords: Vilenkin system, greedy algorithm, Fourier coefficients.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:2, 25–33

UDC: 517.518
Received: 23.12.2011

Citation: M. G. Grigoryan, S. A. Sargsyan, “Nonlinear approximation of functions from the class $L^r$ with respect to the Vilenkin system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 2, 30–39; Russian Math. (Iz. VUZ), 57:2 (2013), 25–33

Citation in format AMSBIB
\Bibitem{GriSar13}
\by M.~G.~Grigoryan, S.~A.~Sargsyan
\paper Nonlinear approximation of functions from the class $L^r$ with respect to the Vilenkin system
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 2
\pages 30--39
\mathnet{http://mi.mathnet.ru/ivm8772}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 2
\pages 25--33
\crossref{https://doi.org/10.3103/S1066369X13020035}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878413837}


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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. M. G. Grigoryan, S. A. Sargsyan, “Almost everywhere convergence of greedy algorithm with respect to Vilenkin system”, J. Contemp. Math. Anal.-Armen. Aca., 53:6 (2018), 331–345  crossref  mathscinet  isi  scopus
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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