7 citations · 11 across the 5 of their papers we have counts for
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On The Spectrum Of Infinite Quantum Graphs
Marco Düfel, James B. Kennedy, Delio Mugnolo +2
We study the interplay between spectrum, geometry and boundary conditions for two distinguished self-adjoint realisations of the Laplacian on infinite metric graphs, the so-called…
On torsional rigidity and ground-state energy of compact quantum graphs
Delio Mugnolo, Marvin Plümer
We develop the theory of torsional rigidity -- a quantity routinely considered for Dirichlet Laplacians on bounded planar domains -- for Laplacians on metric graphs with at least o…
On fully supported eigenfunctions of quantum graphs
Marvin Plümer, Matthias Täufer
We prove that every metric graph which is a tree has an orthonormal sequence of Laplace-eigenfunctions of full support. This implies that the number of nodal domains of the $…
Upper Eigenvalue Bounds for the Kirchhoff Laplacian on Embbeded Metric Graphs
Marvin Plümer
We derive upper bounds for the eigenvalues of the Kirchhoff Laplacian on a compact metric graph depending on the graph's genus g. These bounds can be further improved if , i…