### 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 language | English |
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Pages (from-to) | 1605--1617 |

Journal | Proceedings of the American Mathematical Society |

Volume | 144 |

Issue number | No 4, |

Publication status | Published - 2016 |

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## Cite this

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