{
  "id": "1312.1927",
  "version": "v1",
  "published": "2013-12-06T16:58:56.000Z",
  "updated": "2013-12-06T16:58:56.000Z",
  "title": "New inversion, convolution and Titchmarsh's theorems for the half-Hilbert transform",
  "authors": [
    "Semyon Yakubovich"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the convolution method, which is based on the Mellin-Barnes integrals, we prove the corresponding convolution and Titchmarsh's theorems for the half-Hilbert transform. Some applications to the solvability of a new class of singular integral equations are demonstrated. Our technique does not require the use of methods of the Riemann-Hilbert boundary value problems for analytic functions. The same approach will be applied in the forthcoming research to invert the half-Hartley transform and to establish its convolution theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-06T16:58:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A15",
      "44A35",
      "45E05",
      "45E10"
    ],
    "keywords": [
      "titchmarshs theorems",
      "half-hilbert transform",
      "riemann-hilbert boundary value problems",
      "singular integral equations",
      "reciprocal inverse operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1927Y"
    }
  }
}