### Abstract

We consider Schr¨odinger 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 Schr¨odinger operators and the minimax principle

Original language | English |
---|---|

Pages (from-to) | 3951-3967 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 9 |

Publication status | Published - 2015 |

## Fingerprint Dive into the research topics of 'Spectral band localization for Schrodinger operators on periodic graphs'. Together they form a unique fingerprint.

## Cite this

Korotyaev, E., & Saburova, N. (2015). Spectral band localization for Schrodinger operators on periodic graphs.

*Proceedings of the American Mathematical Society*,*143*(9), 3951-3967.