{
  "id": "1204.2924",
  "version": "v3",
  "published": "2012-04-13T08:57:07.000Z",
  "updated": "2012-09-05T16:46:27.000Z",
  "title": "A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term",
  "authors": [
    "Anke Kalauch",
    "Rainer Picard",
    "Stefan Siegmund",
    "Sascha Trostorff",
    "Marcus Waurick"
  ],
  "comment": "Minor adjustments done",
  "categories": [
    "math.CA"
  ],
  "abstract": "We discuss ordinary differential equations with delay and memory terms in Hilbert spaces. By introducing a time derivative as a normal operator in an appropriate Hilbert space, we develop a new approach to a solution theory covering integro-differential equations, neutral differential equations and general delay differential equations within a unified framework. We show that reasonable differential equations lead to causal solution operators.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-09-05T16:46:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K05",
      "34A40",
      "34A12",
      "45G15"
    ],
    "keywords": [
      "ordinary differential equations",
      "hilbert space perspective",
      "memory term",
      "general delay differential equations",
      "solution theory covering integro-differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2924K"
    }
  }
}