The Krein–von Neumann Extension for Schrödinger Operators on Metric Graphs
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AbstractThe Krein–von Neumann extension is studied for Schrödinger 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.
2016 ◽
Vol 96
(12)
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pp. 2149-2161
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2007 ◽
Vol 253
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pp. 515-533
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2014 ◽
Vol 367
(1)
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pp. 707-724
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2012 ◽
Vol 14
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pp. 357-366
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2012 ◽
Vol 45
(12)
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pp. 125206
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