JournalsjstVol. 4, No. 2pp. 211–219

Rayleigh estimates for differential operators on graphs

  • Pavel Kurasov

    Stockholm University, Sweden
  • Sergey Naboko

    St. Petersburg University, Russian Federation
Rayleigh estimates for differential operators on graphs cover

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