DOI

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.
Язык оригиналаанглийский
Страницы (с-по)1605--1617
ЖурналProceedings of the American Mathematical Society
Том144
Номер выпускаNo 4,
DOI
СостояниеОпубликовано - 2016

ID: 7560953