Estimates of bands for Laplacians on periodic equilateral metric graphs

Korotyaev, Evgeny; Saburova, Natalia

doi:10.1090/proc/12815

Estimates of bands for Laplacians on periodic equilateral metric graphs
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by Evgeny Korotyaev and Natalia Saburova PDF

Proc. Amer. Math. Soc. 144 (2016), 1605-1617 Request permission

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-degenerate 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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