Spectral band localization for Schrodinger operators on periodic graphs

E. Korotyaev, N. Saburova

Research output

Abstract

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
Original languageEnglish
Pages (from-to)3951-3967
JournalProceedings of the American Mathematical Society
Volume143
Issue number9
Publication statusPublished - 2015

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