{
  "id": "2405.09349",
  "version": "v1",
  "published": "2024-05-15T13:58:12.000Z",
  "updated": "2024-05-15T13:58:12.000Z",
  "title": "Optimal constants of smoothing estimates for the 3D Dirac equation",
  "authors": [
    "Makoto Ikoma",
    "Soichiro Suzuki"
  ],
  "comment": "17 pages. arXiv admin note: text overlap with arXiv:2306.08982",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "Recently, Ikoma (2022) considered optimal constants and extremisers for the $2$-dimensional Dirac equation using the spherical harmonics decomposition. Though its argument is valid in any dimensions $d \\geq 2$, the case $d \\geq 3$ remains open since it leads us to too complicated calculation: determining all eigenvalues and eigenvectors of infinite dimensional matrices. In this paper, we give optimal constants and extremisers of smoothing estimates for the $3$-dimensional Dirac equation. In order to prove this, we construct a certain orthonormal basis of spherical harmonics. With respect to this basis, infinite dimensional matrices actually become block diagonal and so that eigenvalues and eigenvectors can be easily found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-15T13:58:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C55",
      "35B65",
      "35Q41",
      "42B10"
    ],
    "keywords": [
      "optimal constants",
      "3d dirac equation",
      "smoothing estimates",
      "infinite dimensional matrices",
      "dimensional dirac equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}