2008/11/05 by А. Г. Бабенко, A. G. Babenko, Babenko, A. G. +2
Engineering · Mathematics · #41A17 #41A44 #42A10 #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #math.CA #msc:41A17 #msc:41A44 #msc:42A10
paper · pdf · doi:10.48550/arxiv.0811.0686
6 pages
arxiv created 2008/11/05 · openalex publication_date 2008/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note is a continuation of our papers [1,2], devoted to L-approximation of characteristic function of (-h, h) by trigonometric polynomials. In the paper [1] the sharp values of the best approximation for the special values of h were found. In [2] we gave the complete solution of the problem for arbitrary values of h. In general case [2] the situation is more deep and results are not so simple as in [1]. For applications to the problem of optimal constants in the Jackson-type inequalities we need, however, results on L-approximation of B-splines and linear combinations of B-splines. Here we present some simple results about L-approximation of B-splines as well as give the the proof of its sharpness for the special values of h.