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.
Cite this article
Jussi Behrndt, Jonathan Rohleder, Titchmarsh–Weyl theory for Schrödinger operators on unbounded domains. J. Spectr. Theory 6 (2016), no. 1, pp. 67–87DOI 10.4171/JST/118