Estimates of bands for Laplacians on periodic equilateral metric graphs

E. Korotyaev, N. Saburova

Research output

2 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)1605--1617
JournalProceedings of the American Mathematical Society
Volume144
Issue numberNo 4,
Publication statusPublished - 2016

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