{
  "id": "1302.1262",
  "version": "v1",
  "published": "2013-02-06T04:28:11.000Z",
  "updated": "2013-02-06T04:28:11.000Z",
  "title": "The Fourier transform and convolutions generated by a differential operator with boundary condition on a segment",
  "authors": [
    "Baltabek Kanguzhin",
    "Niyaz Tokmagambetov"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution explicitly depends on the boundary condition that defines the domain of the operator $L.$ The convolution is closely connected to the inverse operator or to the resolvent. So, we first find a representation for the resolvent, and then introduce the required convolution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-06T04:28:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34B10",
      "34L10",
      "47G30",
      "47E05",
      "J.2"
    ],
    "keywords": [
      "fourier transform",
      "boundary condition",
      "differential operator",
      "convolutions",
      "arbitrary restriction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1262K"
    }
  }
}