2013/10/13 by Korotyaev, Evgeny, Saburova, Natalia
#FOS: Mathematics #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1310.3461
We consider Schrödinger 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 Schrödinger operators and the minimax principle.