58 citations · 919 across the 49 of their papers we have counts for
52 papers
Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge
Gregory Berkolaiko, Denis I. Borisov, Marshall King
We consider a metric graph consisting of two edges, one of which has length which we send to zero. On this graph we study the resolvent and spectrum of the Laplacian…
Exotic eigenvalues of shrinking metric graphs
Gregory Berkolaiko, Yves Colin de Verdière
Eigenvalue spectrum of the Laplacian on a metric graph with arbitrary but fixed vertex conditions is investigated in the limit as the lengths of all edges decrease to zero at the s…
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…
Computing nodal deficiency with a refined Dirichlet-to-Neumann map
Gregory Berkolaiko, Graham Cox, Bernard Helffer +1
Recent work of the authors and their collaborators has uncovered fundamental connections between the Dirichlet-to-Neumann map, the spectral flow of a certain family of self-adjoint…
Universality of nodal count distribution in large metric graphs
Lior Alon, Ram Band, Gregory Berkolaiko
An eigenfunction of the Laplacian on a metric (quantum) graph has an excess number of zeros due to the graph's non-trivial topology. This number, called the nodal surplus, is an in…
Three dimensional elastic beam frames: rigid joint conditions in variational and differential formulation
Gregory Berkolaiko, Mahmood Ettehad
We consider three-dimensional elastic frames constructed out of Euler--Bernoulli beams and describe a simple process of generating joint conditions out of the geometric description…