{
  "id": "math/0410491",
  "version": "v1",
  "published": "2004-10-22T14:34:26.000Z",
  "updated": "2004-10-22T14:34:26.000Z",
  "title": "Tensor algebras and displacement structure. IV. Invariant kernels",
  "authors": [
    "T. Banks",
    "T. Constantinescu",
    "Nermine El-Sissi"
  ],
  "comment": "19 pages, 5 figures",
  "categories": [
    "math.FA",
    "math.CO"
  ],
  "abstract": "In this paper we investigate the class of invariant positive definite kernels on the free semigroup on N generators. We provide a combinatorial description of the positivity of the kernel in terms of Dyck paths and then we find a displacement equation that encodes the invariance property of the kernel.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-22T14:34:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A69",
      "47A57"
    ],
    "keywords": [
      "displacement structure",
      "invariant kernels",
      "tensor algebras",
      "invariant positive definite kernels",
      "free semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10491B"
    }
  }
}