Abstract
We study the order of polynomial approximations of periodic functions on intervals which are internal with respect to the main interval of periodicity and on which these functions are sufficiently smooth. The estimates obtained contain parameters which characterize the smoothness and alternation of signs of nuclear functions and parameters that determine classes of approximated functions.
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References
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M. A. Sukhorol’skii, On the Problem of Approximation of Functions by Averaging Operators [in Russian], Preprint, Science-Educational Center for Mathematical Simulation at the Institute of Applied Problems in Mechanies and Mathematics, Ukrainian Academy of Sciences, L’viv (1995).
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Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp.706–714, May, 1997.
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Sukhorol’skii, M.A. On the order of local approximation of functions by trigonometric polynomials that are partial sums of averaging operators. Ukr Math J 49, 787–797 (1997). https://doi.org/10.1007/BF02486460
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DOI: https://doi.org/10.1007/BF02486460