Integral approximation of the characteristic function of an interval and the Jackson inequality in C()

We apply the results on the integral approximation of the characteristic function of an interval by the subspace of trigonometric polynomials of order at most n − 1, which were obtained by the authors earlier, to investigate the Jackson inequality between the best uniform approximation of a continuo...

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2009-09, Vol.266 (Suppl 1), p.56-63
Main Authors: Babenko, A. G., Kryakin, Yu. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We apply the results on the integral approximation of the characteristic function of an interval by the subspace of trigonometric polynomials of order at most n − 1, which were obtained by the authors earlier, to investigate the Jackson inequality between the best uniform approximation of a continuous periodic function by the subspace and its modulus of continuity of the second order. The corresponding method of the uniform approximation of continuous periodic functions by trigonometric polynomials is constructed.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543809060054