Rayleigh estimates for differential operators on graphs
Pavel Kurasov
Stockholm University, SwedenSergey Naboko
St. Petersburg University, Russian Federation
Abstract
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.
Cite this article
Pavel Kurasov, Sergey Naboko, Rayleigh estimates for differential operators on graphs. J. Spectr. Theory 4 (2014), no. 2, pp. 211–219
DOI 10.4171/JST/67