Titchmarsh-Weyl theory for Schr\"odinger operators on unbounded domains

Jussi Behrndt; Jonathan Rohleder

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arXiv · 1208.5224

Titchmarsh-Weyl theory for Schr\"odinger operators on unbounded domains

Jussi Behrndt·Jonathan Rohleder

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Abstract

In this note it is proved that the complete spectral data of selfadjoint Schr\"odinger 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 analogues of classical facts from singular Sturm-Liouville theory.

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BibTeX RIS

Jussi Behrndt, Jonathan Rohleder. 2012-08-26. Titchmarsh-Weyl theory for Schr\"odinger operators on unbounded domains. https://arxiv.org/abs/1208.5224

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