{
  "id": "1108.2890",
  "version": "v1",
  "published": "2011-08-14T17:03:50.000Z",
  "updated": "2011-08-14T17:03:50.000Z",
  "title": "Some properties of Fourier integrals",
  "authors": [
    "A. F. Grishin",
    "M. V. Skoryk"
  ],
  "comment": "36 pages, in Russian",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let F(R^n) be the algebra of Fourier transforms of functions from L_1(R^n), K(R^n) be the algebra of Fourier transforms of bounded complex Borel measures in R^n and W be Wiener algebra of continuous 2pi-periodic functions with absolutely convergent Fourier series. New properties of functions from these algebras are obtained. Some conditions which determine membership of f in F(R) are given. For many elementary functions f the problem of belonging f to F(R) can be resolved easily using these conditions. We prove that the Hilbert operator is a bijective isometric operator in the Banach spaces W_0, F(R), K(R)-A_1 (A_1 is the one-dimension space of constant functions). We also consider the classes M_k, which are similar to the Bochner classes F_k, and obtain integral representation of the Carleman transform of measures of M_k by integrals of some specific form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-14T17:03:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A38"
    ],
    "keywords": [
      "fourier integrals",
      "properties",
      "fourier transforms",
      "bounded complex borel measures",
      "absolutely convergent fourier series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.2890G"
    }
  }
}