Spectral band localization for Schrödinger operators on periodic graphs

Abstract: We consider Schr\"odinger operators on periodic discrete graphs. It is known that the spectrum of these operators has band structure. We obtain a localization of spectral bands in terms of eigenvalues of Dirichlet and Neumann operators on a finite graph, which is constructed from the fundamental cell of the periodic graph. The proof is based on the Floquet decomposition of Schr\"odinger operators and the minimax principle.