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Mat. Sb., 2012, Volume 203, Number 1, Pages 91–114 (Mi msb7694)  

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

Approximation of periodic functions in the classes $H_q^\Omega$ by linear methods

N. N. Pustovoitov

Moscow State Technical University "MAMI"

Abstract: The following result is proved: if approximations in the norm of $L_\infty$ (of $H_1$) of functions in the classes $H_\infty^\Omega$ (in $H_1^\Omega$, respectively) by some linear operators have the same order of magnitude as the best approximations, then the set of norms of these operators is unbounded. Also Bernstein's and the Jackson-Nikol'skiǐ inequalities are proved for trigonometric polynomials with spectra in the sets $Q(N)$ (in $\varGamma(N,\Omega)$).
Bibliography: 15 titles.

Keywords: modulus of continuity, linear approximations, Bernstein's inequalities, Nikol'skiǐ's inequalities, functions of several variables.

DOI: https://doi.org/10.4213/sm7694

Full text: PDF file (596 kB)
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English version:
Sbornik: Mathematics, 2012, 203:1, 88–110

Bibliographic databases:

UDC: 517.518.832
MSC: 41A35, 42B99
Received: 18.02.2010 and 08.06.2011

Citation: N. N. Pustovoitov, “Approximation of periodic functions in the classes $H_q^\Omega$ by linear methods”, Mat. Sb., 203:1 (2012), 91–114; Sb. Math., 203:1 (2012), 88–110

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Sh. O. Shayanbaeva, “Otsenka normy proizvodnykh $\lambda$-yader Dirikhle”, Mezhdunar. nauch.-issled. zhurn., 2015, no. 6-2(37), 17–19  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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