TY - JOUR

T1 - Spectral band localization for Schrodinger operators on periodic graphs

AU - Korotyaev, E.

AU - Saburova, N.

PY - 2015

Y1 - 2015

N2 - 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

AB - 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

KW - Schrodinger operator

KW - periodic discrete graph

KW - spectral band localization.

M3 - Article

VL - 143

SP - 3951

EP - 3967

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -