Geodesic
Integral approximation of the characteristic function of an interval and the Jackson inequality in $C(\mathbb T)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 59-65 Cet article a éte moissonné depuis la source Math-Net.Ru

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An application of the results about integral approximation of the characteristic function of an interval by the subspace $\tau_{n-1}$ of trigonometric polynomials of order at most $n-1$, which were obtained by the authors earlier, to investigation of the Jackson inequality between the best uniform approximation of a continuous periodic function by the subspace $\tau_{n-1}$ and its modulus of continuity of the second order is presented. A respective method of uniform approximation of continuous periodic functions by trigonometric polynomials is constructed.
Keywords: integral approximation of a function by polynomials, the Jackson inequality. 
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A. G. Babenko; Yu. V. Kryakin. Integral approximation of the characteristic function of an interval and the Jackson inequality in $C(\mathbb T)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 59-65. http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a4/

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