11 papers · 1 filter
Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs
Matthias Hofmann, James B. Kennedy
We prove interlacing inequalities between spectral minimal energies of metric graphs built on Dirichlet and standard Laplacian eigenvalues, as recently introduced in [Kennedy et al…
On Pleijel's nodal domain theorem for quantum graphs
Matthias Hofmann, James B. Kennedy, Delio Mugnolo +1
We establish metric graph counterparts of Pleijel's theorem on the asymptotics of the number of nodal domains of the -th eigenfunction(s) of a broad class of operators on…
A theory of spectral partitions of metric graphs
James B. Kennedy, Pavel Kurasov, Corentin Léna +1
We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus…
Disjointness-preserving operators and isospectral Laplacians
Wolfgang Arendt, James B. Kennedy
All the known counterexamples to Kac' famous question "can one hear the shape of a drum", i.e., does isospectrality of two Laplacians on domains imply that the domains are congruen…
On the eigenvalues of quantum graph Laplacians with large complex couplings
James B. Kennedy, Robin Lang
We study the location of the spectrum of the Laplacian on compact metric graphs with complex Robin-type vertex conditions, also known as conditions, on some or all of the graph…
On the eigenvalues of the Robin Laplacian with a complex parameter
Sabine Bögli, James B. Kennedy, Robin Lang
We study the spectrum of the Robin Laplacian with a complex Robin parameter on a bounded Lipschitz domain . We start by establishing a number of properties of the correspond…