{
  "id": "2202.07338",
  "version": "v1",
  "published": "2022-02-15T11:50:07.000Z",
  "updated": "2022-02-15T11:50:07.000Z",
  "title": "Evolution Equations in Hilbert Spaces via the Lacunae Method",
  "authors": [
    "Maksim V. Kukushkin"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2112.10396",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we consider evolution equations in the abstract Hilbert space under the special conditions imposed on the operator at the right-hand side of the equation. We establish the method that allows us to formulate the existence and uniqueness theorem and find a solution in the form of a series on the root vectors of the right-hand side. As an application we consider fractional differential equations of various kinds. Such operators as the Riemann-Liouville fractional differential operator, the Riesz potential, the difference operator have been involved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-15T11:50:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B28",
      "47A10",
      "47B12",
      "47B10",
      "26A33",
      "39A05"
    ],
    "keywords": [
      "evolution equations",
      "lacunae method",
      "riemann-liouville fractional differential operator",
      "right-hand side",
      "abstract hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}