Hauptmenü
• Autor
• Behrndt, Jussi
• Frank, Rupert L.
• Kühn, Christian
• 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
• Zugriffsrechte
• 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.