The Krein-von Neumann extension for Schr\"odinger operators on metric graphs

Jacob Muller; Jonathan Rohleder

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arXiv · 2006.15091

The Krein-von Neumann extension for Schr\"odinger operators on metric graphs

Jacob Muller·Jonathan Rohleder

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Abstract

The Krein-von Neumann extension is studied for Schr\"odinger operators on metric graphs. Among other things, its vertex conditions are expressed explicitly, and its relation to other self-adjoint vertex conditions (e.g. continuity-Kirchhoff) is explored. A variational characterisation for its positive eigenvalues is obtained. Based on this, the behaviour of its eigenvalues under perturbations of the metric graph is investigated, and so-called surgery principles are established. Moreover, isoperimetric eigenvalue inequalities are obtained.

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BibTeX RIS

Jacob Muller, Jonathan Rohleder. 2020-06-26. The Krein-von Neumann extension for Schr\"odinger operators on metric graphs. https://arxiv.org/abs/2006.15091

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