Abstract
In the space L 2, we study a number of smoothness characteristics of functions; our study is based on the use of the generalized shift operator τ h . For the case inwhich τ is the Steklov operator S, we obtain exact constants in Jackson-type inequalities for some classes of 2π-periodic functions. We also calculate the exact values of the n-widths of function classes defined by the smoothness characteristics under consideration.
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Original Russian Text © S. B. Vakarchuk, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 4, pp. 511–529.
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Vakarchuk, S.B. Generalized smoothness characteristics in Jackson-type inequalities and widths of classes of functions in L 2 . Math Notes 98, 572–588 (2015). https://doi.org/10.1134/S0001434615090254
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DOI: https://doi.org/10.1134/S0001434615090254