{
  "id": "1210.7996",
  "version": "v1",
  "published": "2012-10-30T13:12:48.000Z",
  "updated": "2012-10-30T13:12:48.000Z",
  "title": "Approximation of functions of several variables by linear methods in the space $S^p$",
  "authors": [
    "Viktor V. Savchuk",
    "Andriy L. Shidlich"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "In the spaces $S^p$ of functions of several variables, $2\\pi$-periodic in each variable, we study the approximative properties of operators $A^\\vartriangle_{\\varrho,r}$ and $P^\\vartriangle_{\\varrho,s}$, which generate two summation methods of multiple Fourier series on triangular regions. In particular, in the terms of approximation estimates of these operators, we give a constructive description of classes of functions, whose generalized derivatives belong to the classes $S^pH_\\omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-30T13:12:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B05",
      "26B30",
      "26B35",
      "G.1.2"
    ],
    "keywords": [
      "linear methods",
      "multiple fourier series",
      "summation methods",
      "triangular regions",
      "approximation estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7996S"
    }
  }
}