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Mat. Zametki, 1977, Volume 22, Issue 4, Pages 535–542 (Mi mz8075)  

This article is cited in 11 scientific papers (total in 11 papers)

Best approximations of differentiable functions in the metric of the space $L_2$

L. V. Taikov

Moscow Institute of Forestry Engineering

Abstract: The relation between the best approximations of periodic functions by trigonometric polynomials and the moduli of continuity of their arbitrary derivatives in the metric of the space $L_2$ is studied.

Full text: PDF file (419 kB)

English version:
Mathematical Notes, 1977, 22:4, 789–794

Bibliographic databases:

UDC: 517.6
Received: 17.10.1975

Citation: L. V. Taikov, “Best approximations of differentiable functions in the metric of the space $L_2$”, Mat. Zametki, 22:4 (1977), 535–542; Math. Notes, 22:4 (1977), 789–794

Citation in format AMSBIB
\Bibitem{Tai77}
\by L.~V.~Taikov
\paper Best approximations of differentiable functions in the metric of the space~$L_2$
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 4
\pages 535--542
\mathnet{http://mi.mathnet.ru/mz8075}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=463779}
\zmath{https://zbmath.org/?q=an:0371.41015}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 4
\pages 789--794
\crossref{https://doi.org/10.1007/BF01146425}


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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. M. G. Esmaganbetov, “Widths of classes from $L_2[0,2\pi]$ and the minimization of exact constants in Jackson-type inequalities”, Math. Notes, 65:6 (1999), 689–693  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. M. Sh. Shabozov, “Widths of Classes of Periodic Differentiable Functions in the Space $L_{2}[0,2\pi]$”, Math. Notes, 87:4 (2010), 575–581  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Shabozov M.Sh., Yusupov G.A., “Inequalities between the Best Approximations and Homogenizations of Moduli of Continuity in the Space L-2”, Doklady Mathematics, 82:3 (2010), 892–895  crossref  isi
    4. M. Sh. Shabozov, G. A. Yusupov, “Best Polynomial Approximations in $L_2$ of Classes of $2\pi$-Periodic Functions and Exact Values of Their Widths”, Math. Notes, 90:5 (2011), 748–757  mathnet  crossref  crossref  mathscinet  isi
    5. Shabozov M.Sh. Yusupov G.A., “Widths of Certain Classes of Periodic Functions in l-2”, J. Approx. Theory, 164:7 (2012), 869–878  crossref  isi
    6. Shabozov M.Sh., “Exact Jackson-Stechkin-Type Inequalities for 2 Pi-Periodic Functions in (2) and Widths of Some Classes of Functions”, Ukr. Math. J., 63:10 (2012), 1633–1639  crossref  isi
    7. Shabozov M.Sh., Temurbekova S.D., “Znacheniya poperechnikov klassov funktsii iz $l_{2}[0,2\pi]$ i minimizatsiya tochnykh konstant v neravenstvakh tipa dzheksona”, Izvestiya tulskogo gosudarstvennogo universiteta. estestvennye nauki, 2012, no. 3, 60–68  elib
    8. R. A. Lasuriya, “Jackson-Type Inequalities in the Spaces $S^{(p,q)}(\sigma^{m-1})$”, Math. Notes, 105:5 (2019), 707–719  mathnet  crossref  crossref  mathscinet  isi  elib
    9. Babenko V.F. Konareva S.V., “Jackson-Stechkin-Type Inequalities For the Approximation of Elements of Hilbert Spaces”, Ukr. Math. J., 70:9 (2019), 1331–1344  crossref  isi
    10. M. Sh. Shabozov, “Nekotorye voprosy approksimatsii periodicheskikh funktsii trigonometricheskimi polinomami v $L_2$”, Chebyshevskii sb., 20:4 (2019), 385–398  mathnet  crossref
    11. Vakarchuk S.B., “On the Estimates of Widths of the Classes of Functions Defined By the Generalized Moduli of Continuity and Majorants in the Weighted Space l-2,l-X(0,1)”, Ukr. Math. J., 71:2 (2019), 202–214  crossref  isi
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