The paper presents general theorems for the case of periodic functions, which allow one to obtain estimates on the best approximation by trigonometric polynomials in terms of deviations of aggregates involving values of the function being approximated and its primitives. Some applications are provided. Bibliography: 4 titles.
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V. V. Zhuk, Approximation of Periodic Functions [in Russian], Leningrad (1982).
V. V. Zhuk and V. F. Kuzyutin, Function Approximation and Numerical Integration [in Russian], St.Petersburg (1995).
V. V. Zhuk, “Differential equations with partial derivatives,” in: Mezhvuz. Sb. Nauchn. Trud., St.Petersburg (1992), pp. 74–85.
V. V. Zhuk, “Inequalities for the best approximations of the type of the generalized Jackson theorem,” Zap. Nauchn. Semin. POMI, 404, 135–156 (2012).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 404, 2012, pp. 157–174.
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Zhuk, V.V. Estimates for the best approximations of a periodic function by linear combinations of values of the function and its primitives. J Math Sci 193, 89–99 (2013). https://doi.org/10.1007/s10958-013-1436-0
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DOI: https://doi.org/10.1007/s10958-013-1436-0