{
  "id": "1902.02035",
  "version": "v1",
  "published": "2019-02-06T06:06:14.000Z",
  "updated": "2019-02-06T06:06:14.000Z",
  "title": "A remark on convergence almost-everywhere of eigenfunction expansions of elliptic operators",
  "authors": [
    "Ravshan Ashurov"
  ],
  "comment": "5 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper it is proposed a very simple method for estimating the maximal operator in $L_1$. Using this method one can considerably improve the existing theorems on convergence almost-everywhere of eigenfunction expansions of an arbitrary elliptic differential operators with a point spectrum. In particular, it is obtained a new result on convergence almost-everywhere of spherical partial sums of the multiple Fourier series of smooth functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-06T06:06:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P10",
      "42B05"
    ],
    "keywords": [
      "convergence almost-everywhere",
      "eigenfunction expansions",
      "elliptic operators",
      "arbitrary elliptic differential operators",
      "multiple fourier series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}