In the space L 2 of periodic functions, sharp (in the sense of constants) lower estimates for the deviation of the modified Steklov functions of the first and second orders in terms of the modulus of continuity are established. Similar results are also obtained for even continuous periodic functions with nonnegative Fourier coefficients in the space C. Bibliography: 3 titles.
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V. V. Zhuk and V. F. Kuzyutin, Approximation of Functions and Numerical Integration [in Russian], St. Petersburg (1995).
V. V. Zhuk, Approximation of Periodic Functions [in Russian], Leningrad (1982).
N. K. Bari, Trigonometric Series [in Russian], Moscow (1961).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 429, 2014, pp. 20–33.
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Dron’, V.O., Zhuk, V.V. Approximation of Periodic Functions by Modified Steklov Averages in L 2 . J Math Sci 207, 815–824 (2015). https://doi.org/10.1007/s10958-015-2405-6
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DOI: https://doi.org/10.1007/s10958-015-2405-6