TY - JOUR

T1 - SPECTRAL BAND LOCALIZATION FOR SCHRODINGER OPERATORS ON DISCRETE PERIODIC GRAPHS

AU - Korotyaev, Evgeny

AU - Saburova, Natalia

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

M3 - Article

VL - 143

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -