Estimates of bands for Laplacians on periodic equilateral metric graphs

2013/12/23 by Korotyaev, Evgeny, Saburova, Natalia
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1312.6510

Abstract

We consider Laplacians on periodic equilateral metric graphs. The spectrum of the Laplacian consists of an absolutely continuous part (which is a union of an infinite number of non-degenerated spectral bands) plus an infinite number of flat bands, i.e., eigenvalues of infinite multiplicity. We estimate the Lebesgue measure of the bands on a finite interval in terms of geometric parameters of the graph. The proof is based on spectral properties of discrete Laplacians.

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