7 papers · 1 filter
The Krein-von Neumann extension for Schrödinger operators on metric graphs
Jacob Muller, Jonathan Rohleder
The 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…
Quantum trees which maximize higher eigenvalues are unbalanced
Jonathan Rohleder
The isoperimetric problem of maximizing all eigenvalues of the Laplacian on a metric tree graph within the class of trees of a given average edge length is studied. It turns out th…
Inequalities between Neumann and Dirichlet eigenvalues of Schrödinger operators
Jonathan Rohleder
Given a Schrödinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann a…
Laplacians on bipartite metric graphs
Pavel Kurasov, Jonathan Rohleder
We study spectral properties of the standard (also called Kirchhoff) Laplacian and the anti-standard (or anti-Kirchhoff) Laplacian on a finite, compact metric graph. We show that t…
On the hot spots of quantum trees
James Kennedy, Jonathan Rohleder
We show that any second eigenfunction of the Laplacian with standard vertex conditions on a metric tree graph attains its extremal values only at degree one vertices, and give an e…
Spectral monotonicity for Schrödinger operators on metric graphs
Jonathan Rohleder, Christian Seifert
We study the influence of certain geometric perturbations on the spectra of self-adjoint Schrödinger operators on compact metric graphs. Results are obtained for permutation invari…