{
  "id": "1703.01708",
  "version": "v1",
  "published": "2017-03-06T02:38:50.000Z",
  "updated": "2017-03-06T02:38:50.000Z",
  "title": "Inverse resonance problems for the Schrödinger operator on the real line with mixed given data",
  "authors": [
    "Xiao-Chuan Xu",
    "Chuan-Fu Yang"
  ],
  "comment": "11 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this work, we study inverse resonance problems for the Schr\\\"odinger operator on the real line with the potential supported in $[0,1]$. In general, all eigenvalues and resonances can not uniquely determine the potential (Zworski, SIAM J. Math. Anal. 32, 2001). (i) It is shown that if the potential is known a priori on $[0,1/2]$, then the unique recovery of the potential on the whole interval from all eigenvalues and resonances is valid. (ii) If the potential is known a priori on $[0,a]$, then for the case $a>1/2$, infinitely many eigenvalues and resonances can be missing for the unique determination of the potential, and for the case $a<1/2$, all eigenvalues and resonances plus a part of so-called sign-set can uniquely determine the potential. (iii) It is also shown that all eigenvalues and resonances, together with a set of logarithmic derivative values of eigenfunctions and wave-functions at $1/2$, can uniquely determine the potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-06T02:38:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A55",
      "34L25",
      "47E05"
    ],
    "keywords": [
      "real line",
      "schrödinger operator",
      "eigenvalues",
      "uniquely determine",
      "study inverse resonance problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}