Journal of Spectral Theory

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Volume 4, Issue 2, 2014, pp. 211–219
DOI: 10.4171/JST/67

Published online: 2014-07-13

Rayleigh estimates for differential operators on graphs

Pavel Kurasov[1] and Sergey Naboko[2]

(1) Stockholm University, Sweden
(2) St. Petersburg University, Russian Federation

We study the spectral gap, i.e. the distance between the two lowest eigenvalues for Laplace operators on metric graphs. A universal lower estimate for the spectral gap is proven and it is shown that it is attained if the graph is formed by just one interval. Uniqueness of the minimizer allows to prove a geometric version of the Ambartsumian theorem derived originally for Schrödinger operators.

Keywords: Quantum graph, Eulerian path, spectral gap

Kurasov Pavel, Naboko Sergey: Rayleigh estimates for differential operators on graphs. J. Spectr. Theory 4 (2014), 211-219. doi: 10.4171/JST/67