58 citations · 919 across the 49 of their papers we have counts for
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math-ph2010★ 19 cited
Dynamics of nodal points and the nodal count on a family of quantum graphs
Ram Band, Gregory Berkolaiko, Uzy Smilansky
We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schrödinger-type differential operator). Using tools such as scattering app…
math-ph2010★ 2 cited
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths
Gregory Berkolaiko, Peter Kuchment
We study the dependence of the quantum graph Hamiltonian, its resolvent, and its spectrum on the vertex conditions and graph edge lengths. In particular, several results on the int…