### Abstract

We consider Schrodinger operators on periodic discrete graphs. It is known that the spectrum of these operators has band structure. We describe a localization of spectral bands and estimate the Lebesgue measure of the spectrum in terms of eigenvalues of Dirichlet and Neumann operators on a fundamental domain of the periodic graph. The proof is based on the Floquet decomposition of Schrodinger operators and the minimax principle.

Original language | English |
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Number of pages | 17 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 9 |

Publication status | Published - 2015 |

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## Cite this

Korotyaev, E., & Saburova, N. (2015). SPECTRAL BAND LOCALIZATION FOR SCHRODINGER OPERATORS ON DISCRETE PERIODIC GRAPHS.

*Proceedings of the American Mathematical Society*,*143*(9).