{
  "id": "0811.0686",
  "version": "v1",
  "published": "2008-11-05T10:08:09.000Z",
  "updated": "2008-11-05T10:08:09.000Z",
  "title": "$L$-approximation of $B$-splines by trigonometric polynomials",
  "authors": [
    "A. G. Babenko",
    "Yu. V. Kryakin"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "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 $h$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-05T10:08:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A17",
      "41A44",
      "42A10"
    ],
    "keywords": [
      "trigonometric polynomials",
      "special values",
      "characteristic function",
      "optimal constants",
      "sharp values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.0686B"
    }
  }
}