{
  "id": "1704.06056",
  "version": "v1",
  "published": "2017-04-20T08:56:40.000Z",
  "updated": "2017-04-20T08:56:40.000Z",
  "title": "On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness",
  "authors": [
    "Nimete Sh. Berisha",
    "Faton M. Berisha",
    "Mikhail K. Potapov",
    "Marjan Dema"
  ],
  "comment": "18 pages. arXiv admin note: substantial text overlap with arXiv:1208.6123",
  "journal": "Abstract and Applied Analysis, Volume 2017 (2017), Article ID 9323181, 11 pp",
  "doi": "10.1155/2017/9323181",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we give a characterization of Nikol'ski\\u{\\i}-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to a such a class are given. In order to prove our results, we make use of certain recent reverse Copson- and Leindler-type inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-20T08:56:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A10",
      "42A16"
    ],
    "keywords": [
      "trigonometric polynomials",
      "smoothness",
      "approximations",
      "lacunary fourier coefficients",
      "type classes"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Hindawi",
      "journal": "Adv. High Energ. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}