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Spectral theory for Schrödinger operators with δ-interactions supported on curves in ℝ³
Citation Link: https://doi.org/10.15480/882.1775
Publikationstyp
Journal Article
Date Issued
2016-11-21
Sprache
English
Institut
TORE-DOI
Journal
Volume
18
Issue
4
Start Page
1305
End Page
1347
Citation
Annales Henri Poincaré 4 (18): 1305-1347 (2016)
Publisher DOI
Scopus ID
Publisher
Springer
The main objective of this paper is to systematically develop a spectral and scattering theory for self-adjoint Schrödinger operators with δ-interactions supported on closed curves in R3. 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.
Subjects
Schrödinger operators
DDC Class
510: Mathematik
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