{
  "id": "1505.03311",
  "version": "v1",
  "published": "2015-05-13T10:24:39.000Z",
  "updated": "2015-05-13T10:24:39.000Z",
  "title": "The $α$-orthogonal complements of regular subspaces of 1-dim Brownian motion",
  "authors": [
    "Liping Li",
    "Xiucui Song"
  ],
  "comment": "8 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Roughly speaking, a regular subspace of a Dirichlet form is a subspace, which is also a regular Dirichlet form, on the same state space. In particular, the domain of regular subspace is a closed subspace of the Hilbert space induced by the domain and $\\alpha$-inner product of original Dirichlet form. We shall investigate the orthogonal complement of regular subspace of 1-dimensional Brownian motion in this paper. Our main results indicate that this orthogonal complement has a very close connection with the $\\alpha$-harmonic equation under Neumann boundary condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-13T10:24:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C25",
      "60J55",
      "60J60"
    ],
    "keywords": [
      "regular subspace",
      "orthogonal complement",
      "brownian motion",
      "original dirichlet form",
      "regular dirichlet form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150503311L"
    }
  }
}