Abstract
We investigate the asymptotic behavior of the upper bounds of deviations of linear means of Fourier series from the classes \(C_\infty ^{\psi}\). In particular, we obtain asymptotic equalities that give a solution of the Kolmogorov–Nikol'skii problem for the de la Vallée-Poussin sums on the classes \(C_\infty ^{\overline \psi }\).
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Rukasov, V.I., Chaichenko, S.O. Approximation of \(\overline \psi\)-Integrals of Periodic Functions by de la Vallée-Poussin Sums (Low Smoothness). Ukrainian Mathematical Journal 53, 1998–2013 (2001). https://doi.org/10.1023/A:1015438922822
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DOI: https://doi.org/10.1023/A:1015438922822