{
  "id": "2208.03748",
  "version": "v1",
  "published": "2022-08-07T15:05:34.000Z",
  "updated": "2022-08-07T15:05:34.000Z",
  "title": "Fourier analysis in spaces of shifts",
  "authors": [
    "A. Yu. Ulitskaya"
  ],
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this paper, we develop a continual analog of decomposition over orthogonal bases in spaces generated by equidistant shifts of a single function. By doing so, we obtain an explicit expression for best approximation by spaces of shifts in $L_2(\\mathbb{R})$. The result is formulated in terms of classical Fourier transform and tends to have various applications in approximation by spaces of shifts and, in particular, in spline approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-07T15:05:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A38",
      "41A30"
    ],
    "keywords": [
      "fourier analysis",
      "classical fourier transform",
      "continual analog",
      "spline approximation",
      "best approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}