{
  "id": "1912.01998",
  "version": "v1",
  "published": "2019-12-03T10:53:47.000Z",
  "updated": "2019-12-03T10:53:47.000Z",
  "title": "On the Gaussian functions of two discrete variables",
  "authors": [
    "Nicolae Cotfas"
  ],
  "comment": "9 pages, 1 figure. For more details see the section \"Documente\" at https://unibuc.ro/user/nicolae.cotfas/",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "A remarkable discrete counterpart of the Gaussian function of one continuous variable can be defined by using a Jacobi theta function, that is, as the sum of a convergent series. We extend this approach to Gaussian functions of two variables, and investigate the Fourier transform and Wigner function of the functions of discrete variable defined in this way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-03T10:53:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q99"
    ],
    "keywords": [
      "gaussian function",
      "discrete variable",
      "jacobi theta function",
      "discrete counterpart",
      "convergent series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}