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

O. O. Novikov, O. G. Rovenska


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.


Kolmogorov-Hikol'skii problem, $(\psi,\beta)$-derivative, right-angled Fourier sums

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