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  • Autor
    • Behrndt, Jussi
    • Frank, Rupert L.
    • Kühn, Christian
    • Lotoreichik, Vladimir
    • Rohleder, Jonathan
  • TitelSpectral Theory for Schrödinger Operators with \(\delta\)-Interactions Supported on Curves in \(\mathbb{R}^3\)
  • Datei
  • DOI10.1007/s00023-016-0532-3
  • Persistent Identifier
  • Erschienen inAnnales Henri Poincaré
  • Band18
  • Erscheinungsjahr2017
  • Heft4
  • Seiten1305-1347
  • ISSN1424-0661
  • ZugriffsrechteCC-BY
  • Download Statistik284
  • Peer ReviewNein
  • AbstractThe main objective of this paper is to systematically develop a spectral and scattering theory for self-adjoint Schrödinger operators with \(\delta\)-interactions supported on closed curves in \(\mathbb{R}^3\). We provide bounds for the number of negative eigenvalues depending on the geometry of the curve, prove an isoperimetric inequality for the principal eigenvalue, derive Schatten--von Neumann properties for the resolvent difference with the free Laplacian, and establish an explicit representation for the scattering matrix.