Abstract
Sharp inequalities are obtained in the space L2, connecting the best approximations of differentiable 2π-periodic functions by trigonometric polynomials with integrals containing the higher-order moduli of continuity of the derivatives of these functions. The Kolmogorov widths of certain classes of functions, defined by these moduli of continuity, are computed.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 125–129, January, 1991.
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Shalaev, V.V. Widths in L2 of classes of differentiable functions, defined by higher-order moduli of continuity. Ukr Math J 43, 104–107 (1991). https://doi.org/10.1007/BF01066914
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DOI: https://doi.org/10.1007/BF01066914