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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.

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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
\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
\jour Math. Notes
\yr 1967
\vol 2
\issue 5
\pages 803--808

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    This publication is cited in the following articles:
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