{
  "id": "2003.08106",
  "version": "v1",
  "published": "2020-03-18T09:14:09.000Z",
  "updated": "2020-03-18T09:14:09.000Z",
  "title": "Analytic hypoellipticity of Keldysh operators",
  "authors": [
    "Jeffrey Galkowski",
    "Maciej Zworski"
  ],
  "comment": "24 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider Keldysh-type operators, $ P = x_1 D_{x_1}^2 + a (x) D_{x_1} + Q (x, D_{x'} ) $, $ x = ( x_1, x') $ with analytic coefficients, and with $ Q ( x, D_{x'} ) $ second order, principally real and elliptic in $ D_{x'} $ for $ x $ near zero. We show that if $ P u =f $, $ u \\in C^\\infty $, and $ f $ is analytic in a neighbourhood of $ 0 $ then $ u $ is analytic in a neighbourhood of $ 0 $. This is a consequence of a microlocal result valid for operators of any order with Lagrangian radial sets. Our result proves a generalized version of a conjecture made by the second author and Lebeau and has applications to scattering theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-18T09:14:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "keldysh operators",
      "analytic hypoellipticity",
      "lagrangian radial sets",
      "microlocal result valid",
      "analytic coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}