The Krein-von Neumann extension for Schr\"odinger operators on metric graphs
Spectral Theory
2020-12-18 v2 Mathematical Physics
Functional Analysis
math.MP
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.
Keywords
Cite
@article{arxiv.2006.15091,
title = {The Krein-von Neumann extension for Schr\"odinger operators on metric graphs},
author = {Jacob Muller and Jonathan Rohleder},
journal= {arXiv preprint arXiv:2006.15091},
year = {2020}
}