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.
|Number of pages||17|
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - 2015|