{
  "id": "2307.12611",
  "version": "v1",
  "published": "2023-07-24T08:38:09.000Z",
  "updated": "2023-07-24T08:38:09.000Z",
  "title": "Fourier series for nonperiodic functions",
  "authors": [
    "Rodrigo López Pouso"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We introduce a small change in the definition of the Fourier series so that we can guarantee the coincidence with the given function at the endpoints of the interval even if the function does not assume the same value at the endpoints. This definition of the Fourier series also wipes out the Gibbs phenomenom at the endpoints of the interval and proves useful in the resolution of antiperiodic boundary value problems with linear partial differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-24T08:38:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A16",
      "42A20",
      "35C10"
    ],
    "keywords": [
      "fourier series",
      "nonperiodic functions",
      "antiperiodic boundary value problems",
      "linear partial differential equations",
      "small change"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}