SPECTRAL BAND LOCALIZATION FOR SCHRODINGER OPERATORS ON DISCRETE PERIODIC GRAPHS

Evgeny Korotyaev, Natalia Saburova

Research output

12 Citations (Scopus)

Abstract

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.
Original languageEnglish
Number of pages17
JournalProceedings of the American Mathematical Society
Volume143
Issue number9
Publication statusPublished - 2015

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