- 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
- Download Statistik1413
- 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.
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