38 citations · 164 across the 11 of their papers we have counts for
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math-ph2008★ 6 cited
Exterior-Interior Duality for Discrete Graphs
Uzy Smilansky
The Exterior-Interior duality expresses a deep connection between the Laplace spectrum in bounded and connected domains in , and the scattering matrices in the exteri…
math-ph2008★ 10 cited
Degeneracies in the length spectra of metric graphs
U. Gavish, U. Smilansky
The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate s…
nlin.CD2008★ 15 cited
Counting nodal domains on surfaces of revolution
Panos D. Karageorge, Uzy Smilansky
We consider eigenfunctions of the Laplace-Beltrami operator on special surfaces of revolution. For this separable system, the nodal domains of the (real) eigenfunctions form a chec…