scholarly journals Wigner-von Neumann type perturbations of periodic Schrödinger operators

2014 ◽  
Vol 367 (1) ◽  
pp. 707-724 ◽  
Author(s):  
Milivoje Lukic ◽  
Darren C. Ong
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Von Neumann ◽  
Neumann Type

scholarly journals The Krein–von Neumann Extension for Schrödinger Operators on Metric Graphs

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Jacob Muller ◽  
Jonathan Rohleder
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Metric Graphs ◽  
Von Neumann ◽  
Metric Graph

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.

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