58 citations · 919 across the 49 of their papers we have counts for
5 papers · 1 filter
Spectral shift via "lateral" perturbation
G. Berkolaiko, P. Kuchment
We consider a compact perturbation of a self-adjoint operator with an eigenvalue below its essential spectrum and the corresponding eigenfunctio…
Convergence of moments of twisted COE matrices
Gregory Berkolaiko, Laura Booton
We investigate eigenvalue moments of matrices from Circular Orthogonal Ensemble multiplicatively perturbed by a permutation matrix. More precisely we investigate variance of the su…
A local test for global extrema in the dispersion relation of a periodic graph
Gregory Berkolaiko, Yaiza Canzani, Graham Cox +1
We consider a family of periodic tight-binding models (combinatorial graphs) that have the minimal number of links between copies of the fundamental domain. For this family we esta…
Degenerate band edges in periodic quantum graphs
Gregory Berkolaiko, Minh Kha
Edges of bands of continuous spectrum of periodic structures arise as maxima and minima of the dispersion relation of their Floquet--Bloch transform. It is often assumed that the e…
Locating conical degeneracies in the spectra of parametric self-adjoint matrices
Gregory Berkolaiko, Advait Parulekar
A simple iterative scheme is proposed for locating the parameter values for which a 2-parameter family of real symmetric matrices has a double eigenvalue. The convergence is proved…