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.
|Journal||Proceedings of the American Mathematical Society|
|Issue number||No 4,|
|Publication status||Published - 2016|
Korotyaev, E., & Saburova, N. (2016). Estimates of bands for Laplacians on periodic equilateral metric graphs. Proceedings of the American Mathematical Society, 144(No 4,), 1605--1617. http://dx.doi.org/10.1090/proc/12815