{
  "id": "1605.02456",
  "version": "v1",
  "published": "2016-05-09T07:45:24.000Z",
  "updated": "2016-05-09T07:45:24.000Z",
  "title": "On the structure of finitely generated shift-invariant subspaces",
  "authors": [
    "K. S. Kazarian"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an element of the finitely generated shift-invariant subspace as a linear combination of Fourier transformations of generators. An estimate for the norms of those coefficients is derived. For the proof a sort of orthogonalization procedure for generators is used which reminds the well known Gram-Schmidt orthogonalization process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-09T07:45:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A30",
      "41A63",
      "42C30"
    ],
    "keywords": [
      "finitely generated shift-invariant subspace",
      "generators",
      "gram-schmidt orthogonalization process",
      "coefficients",
      "fourier transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}