Approximation of the periodical functions of high smoothness by the right-angled linear means of Fourier series

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We obtain asymptotic equalities for upper bounds of the deviations of the right-angled de la Vallee Poussin sums taken over classes of periodical functions of many variables of high smoothness. These equalities guarantee the solvability of the Kolmogorov–Nikol’skii problem for the right-angled de la Vallee Poussin sums on the specified classes of functions.

Keywords: (ψ,β)-derivative, the right-angled de la Vallee Poussin sums, Kolmogorov–Nikol'skiy problem
Citation in English: Rovenska O.G., Novikov O.A. Approximation of the periodical functions of high smoothness by the right-angled linear means of Fourier series // Computer Research and Modeling, 2012, vol. 4, no. 3, pp. 521-529
Citation in English: Rovenska O.G., Novikov O.A. Approximation of the periodical functions of high smoothness by the right-angled linear means of Fourier series // Computer Research and Modeling, 2012, vol. 4, no. 3, pp. 521-529
DOI: 10.20537/2076-7633-2012-4-3-521-529
According to Crossref, this article is cited by:
  • Olga G Rovenska. Approximation of analytic functions by repeated de la Vallee Poussin sums. // Computer Research and Modeling. 2019. — V. 11, no. 3. — P. 367. DOI: 10.20537/2076-7633-2019-11-3-367-377
  • Oleg Aleksandrovich Novikov, Olga G Rovenska. Approximation of classes of Poisson integrals by Fejer sums. // Computer Research and Modeling. 2015. — V. 7, no. 4. — P. 813. DOI: 10.20537/2076-7633-2015-7-4-813-819
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Citations: 2 (RSCI).

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