2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173246This 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 $h$.6 pagesClassical Analysis and ODEs41A17, 41A44, 42A10text