65 citations · 295 across the 21 of their papers we have counts for
5 papers · 2 filters
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…
On the hot spots of quantum graphs
James B. Kennedy, Jonathan Rohleder
We undertake a systematic investigation of the maxima and minima of the eigenfunctions associated with the first nontrivial eigenvalue of the Laplacian on a metric graph equipped w…
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…