$L$-approximation of $B$-splines by trigonometric polynomials
| dc.creator | Babenko, A. G. | |
| dc.creator | Kryakin, Yu. V. | |
| dc.date | 2008-11-05 | |
| dc.date.accessioned | 2026-07-07T10:15:40Z | |
| dc.date.available | 2026-07-07T10:15:40Z | |
| dc.description | 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 $h$. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/0811.0686 | |
| dc.identifier | http://arxiv.org/abs/0811.0686 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173246 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 41A17, 41A44, 42A10 | |
| dc.title | $L$-approximation of $B$-splines by trigonometric polynomials | |
| dc.type | text |