Approximation of the periodical functions of high smoothness by the rightangled Fourier sums

  • O.O. Novikov Slavyansk State Pedagogical University, 19 Batiuka str., 84116, Slavyansk, Ukraine
  • O.G. Rovenska Slavyansk State Pedagogical University, 19 Batiuka str., 84116, Slavyansk, Ukraine
https://doi.org/10.15330/cmp.5.1.102-109
Keywords: Kolmogorov-Hikol'skii problem, $(\psi, \beta)$-derivative, right-angled Fourier sums
Published online: 2013-06-20

Abstract


We obtain asymptotic equalities for upper bounds of the deviations of the right-angled Fourier sums taken over classes of periodical functions of two variables of high smoothness. These equalities in corresponding cases guarantee the solvability of the Kolmogorov–Nikol’skii problem for the right-angled Fourier sums on the specified classes of functions.

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How to Cite
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Novikov O., Rovenska O. Approximation of the Periodical Functions of High Smoothness by the Rightangled Fourier Sums. Carpathian Math. Publ. 2013, 5 (1), 102-109.