58 citations · 919 across the 49 of their papers we have counts for
5 papers · 1 filter
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…
Limits of Quantum Graph Operators With Shrinking Edges
Gregory Berkolaiko, Yuri Latushkin, Selim Sukhtaiev
We address the question of convergence of Schrödinger operators on metric graphs with general self-adjoint vertex conditions as lengths of some of graph's edges shrink to zero. We…
Nodal deficiency, spectral flow, and the Dirichlet-to-Neumann map
Gregory Berkolaiko, Graham Cox, Jeremy L. Marzuola
It was recently shown that the nodal deficiency of an eigenfunction is encoded in the spectrum of the Dirichlet-to-Neumann operators for the eigenfunction's positive and negative n…
Graph Reconstruction from Path Correlation Data
Gregory Berkolaiko, Nick Duffield, Mahmood Ettehad +1
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infe…
Maximal scarring for eigenfunctions of quantum graphs
Gregory Berkolaiko, Brian Winn
We prove the existence of scarred eigenstates for star graphs with scattering matrices at the central vertex which are either a Fourier transform matrix, or a matrix that prohibits…