65 citations · 295 across the 21 of their papers we have counts for
19 papers · 1 filter
On domain monotonicity of Neumann eigenvalues of convex domains
Pedro Freitas, James B. Kennedy
Inspired by a recent result of Funano's, we provide a sharp quantitative comparison result between the first nontrivial eigenvalues of the Neumann Laplacian on bounded convex domai…
Spectral minimal partitions of unbounded metric graphs
Matthias Hofmann, James B. Kennedy, Andrea Serio
We investigate the existence or non-existence of spectral minimal partitions of unbounded metric graphs, where the operator applied to each of the partition elements is a Schröding…
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…
Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap
Gregory Berkolaiko, James B. Kennedy, Pavel Kurasov +1
We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based…
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…
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…
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…
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…
A family of diameter-based eigenvalue bounds for quantum graphs
J. B. Kennedy
We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in…
Surgery principles for the spectral analysis of quantum graphs
Gregory Berkolaiko, James B. Kennedy, Pavel Kurasov +1
We present a systematic collection of spectral surgery principles for the Laplacian on a metric graph with any of the usual vertex conditions (natural, Dirichlet or -type), whic…
Edge connectivity and the spectral gap of combinatorial and quantum graphs
Gregory Berkolaiko, James B. Kennedy, Pavel Kurasov +1
We derive a number of upper and lower bounds for the first nontrivial eigenvalue of a finite quantum graph in terms of the edge connectivity of the graph, i.e., the minimal number…
Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator
Pedro Freitas, James B. Kennedy
We derive explicit inequalities for sums of eigenvalues of one-dimensional Schrödinger operators on the whole line. In the case of the perturbed harmonic oscillator, these bounds c…
Summation formula inequalities for eigenvalues of Schrödinger operators
Pedro Freitas, James B. Kennedy
We derive inequalities for sums of eigenvalues of Schrödinger operators on finite intervals and tori. In the first of these cases, the inequalities converge to the classical trace…
On the Spectral Gap of a Quantum Graph
James B. Kennedy, Pavel Kurasov, Gabriela Malenova +1
We consider the problem of finding universal bounds of "isoperimetric" or "isodiametric" type on the spectral gap of the Laplacian on a metric graph with natural boundary condition…
Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian
Pedro R. S. Antunes, Pedro Freitas, James B. Kennedy
We consider the problem of minimising the eigenvalue of the Robin Laplacian in . Although for and a positive boundary parameter it is known tha…