output
19972022
most citedOn the metric operator for the imaginary cubic oscillator

121 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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9 papers · 1 filter

math.SP2022★ 2 cited

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…

math.SP2022★ 5 cited

Families of non-tiling domains satisfying Pólya's conjecture

Pedro Freitas, Isabel Salavessa

We show the existence of classes of non-tiling domains satisfying Pólya's conjecture in any dimension, in both the Euclidean and non-Euclidean cases. This is a consequence of a mor…

math.SP2021★ 2 cited

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…

math.SP2020★ 12 cited

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…

math.SP2020★ 14 cited

A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities

Pedro R. S. Antunes, Rafael D. Benguria, Vladimir Lotoreichik +1

We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of . Motivated by spectral geometric inequali…

math.SP2018

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…

math.SP2018★ 57 cited

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…

math.SP2018★ 13 cited

The damped wave equation with unbounded damping

Pedro Freitas, Petr Siegl, Christiane Tretter

We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a cont…

math.SP2017★ 40 cited

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…