Geodesic
Estimates of best approximations of periodic function by linear combinations values of the function itself and its primitives
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 157-174
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The general theorems which allow to obtain some estimates of best approximations of periodic function by deviations of aggregates composed of approximated function and its primitives are established. Several examples of applications are given. 
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V. V. Zhuk. Estimates of best approximations of periodic function by linear combinations values of the function itself and its primitives. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 157-174. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a8/

[1] V. V. Zhuk, Approksimatsiya periodcheskikh funktsii, L., 1982 | MR

[2] V. V. Zhuk, V. F. Kuzyutin, Approksimatsiya funktsii i chislennoe integrirovanie, S.-Peterburg, 1995 | MR

[3] V. V. Zhuk, “Differentsialnye uravneniya s chastnymi proizvodnymi”, Mezhvuzovskii sbornik nauchnykh trudov, S.-Peterburg, 1992, 74–85

[4] V. V. Zhuk, “Neravenstva dlya nailuchshikh priblizhenii tipa obobschennoi teoremy Dzheksona”, Zap. nauchn. semin. POMI, 404, 2012, 135–156