JournalsjstVol. 6, No. 1pp. 67–87

Titchmarsh–Weyl theory for Schrödinger operators on unbounded domains

  • Jussi Behrndt

    TU Graz, Austria
  • Jonathan Rohleder

    TU Graz, Austria
Titchmarsh–Weyl theory for Schrödinger operators on unbounded domains cover
Download PDF

Abstract

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. 67–87

DOI 10.4171/JST/118