Journal of Spectral Theory
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Published online: 2016-04-04
Titchmarsh–Weyl theory for Schrödinger operators on unbounded domainsJussi Behrndt and Jonathan Rohleder (1) TU Graz, Austria
(2) TU Graz, Austria
In this paper it is proved that the complete spectral data of selfadjoint Schrödinger operators on unbounded domains can be described with an associated Dirichlet-to-Neumann map. In particular, a characterization of the isolated and embedded eigenvalues, the corresponding eigenspaces, as well as the continuous and absolutely continuous spectrum in terms of the limiting behaviour of the Dirichlet-to-Neumann map is obtained. Furthermore, a sufficient criterion for the absence of singular continuous spectrum is provided. The results are natural multidimensional analogs of classical facts from singular Sturm-Liouville theory.
Keywords: Dirichlet-to-Neumann map, Schrödinger operator, spectrum, Titchmarsh–Weyl function
Behrndt Jussi, Rohleder Jonathan: Titchmarsh–Weyl theory for Schrödinger operators on unbounded domains. J. Spectr. Theory 6 (2016), 67-87. doi: 10.4171/JST/118