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Mat. Zametki, 1967, Volume 2, Issue 5, Pages 513–522 (Mi mz5514)  

This article is cited in 62 scientific papers (total in 63 papers)

The best approximation of periodic functions by trigonometric polynomials in $L^2$

N. I. Chernykh


Abstract: Estimates are gotten for the best approximations in $L_2(0,2\pi)$ of a periodic function by trigonometric polynomials in terms of its $m$-th continuity modulus or in terms of the continuity modulus of its $r$-th derivative. The inequality
$$ E_{n-1}(f)_{L_2}<(C_{2m}^m)^{-1/2}\omega_m(2\pi/n;f)_{L_2} \qquad (f\ne\mathrm{const}) $$
is proved, where the constant $(C_{2m}^m)^{-1/2}$ is unimprovable for the whole space $L_2(0,2\pi)$. Two titles are cited in the bibliography.

Full text: PDF file (506 kB)

English version:
Mathematical Notes, 1967, 2:5, 803–808

Bibliographic databases:

Document Type: Article
UDC: 517.5
Received: 23.01.1967

Citation: N. I. Chernykh, “The best approximation of periodic functions by trigonometric polynomials in $L^2$”, Mat. Zametki, 2:5 (1967), 513–522; Math. Notes, 2:5 (1967), 803–808

Citation in format AMSBIB
\Bibitem{Che67}
\by N.~I.~Chernykh
\paper The best approximation of periodic functions by trigonometric polynomials in~$L^2$
\jour Mat. Zametki
\yr 1967
\vol 2
\issue 5
\pages 513--522
\mathnet{http://mi.mathnet.ru/mz5514}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=221187}
\zmath{https://zbmath.org/?q=an:0167.05002|0162.36102}
\transl
\jour Math. Notes
\yr 1967
\vol 2
\issue 5
\pages 803--808
\crossref{https://doi.org/10.1007/BF01093942}


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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. N. P. Korneichuk, “On extremal problems in the theory of best approximation”, Russian Math. Surveys, 29:3 (1974), 7–43  mathnet  crossref  mathscinet  zmath
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    5. A. G. Babenko, “Sharp Jackson–Stechkin inequality in $L^2$ for multidimensional spheres”, Math. Notes, 60:3 (1996), 248–263  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. A. Yudin, “Two external problems for trigonometric polynomials”, Sb. Math., 187:11 (1996), 1721–1736  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. V. A. Yudin, “Lower bounds for spherical designs”, Izv. Math., 61:3 (1997), 673–683  mathnet  crossref  crossref  mathscinet  zmath  isi
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