{
  "id": "1301.2690",
  "version": "v2",
  "published": "2013-01-12T15:00:34.000Z",
  "updated": "2014-10-22T14:06:42.000Z",
  "title": "Exponential decay of measures and Tauberian theorems",
  "authors": [
    "Ante Mimica"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We study behavior of a measure on $[0,\\infty)$ by considering its Laplace transform. If it is possible to extend the Laplace transform to a complex half-plane containing the imaginary axis, then the exponential decay of the tail of the measure occurs and under certain assumptions we show that the rate of the decay is given by the so called abscissa of convergence and extend the result of Nakagawa from [Nak05]. Under stronger assumptions we give behavior of density of the measure by considering its Laplace transform. In situations when there is no exponential decay we study occurrence of heavy tails and give an application in the theory of non-local equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-12T15:00:34.000Z",
      "title": "Laplace transforms and exponential behavior of representing measures",
      "abstract": "In this article behavior of measures on $[0,\\infty)$ is studied by considering their Laplace transforms. We present a unified approach that covers many cases when Karamata's and de Haan's Tauberian theorems apply. If the Laplace transform can be extended to a complex half-plane containing the imaginary axis, we prove that the tail of the representing measure has exponential decay and establish the precise rate of the decay. We translate this result to the language of Bernstein functions and give two applications in the theory of non-local equations.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-22T14:06:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B10",
      "44A10",
      "47G20",
      "45K05",
      "47G30",
      "40E05"
    ],
    "keywords": [
      "laplace transform",
      "representing measure",
      "exponential behavior",
      "article behavior",
      "complex half-plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.2690M"
    }
  }
}