Spectral band localization for Schrödinger operators on discrete periodic graphs
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- by Evgeny Korotyaev and Natalia Saburova PDF
- Proc. Amer. Math. Soc. 143 (2015), 3951-3967 Request permission
Abstract:
We consider Schrödinger 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 Schrödinger operators and the minimax principle.References
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Additional Information
- Evgeny Korotyaev
- Affiliation: Department of Mathematical Physics, Faculty of Physics, St. Petersburg State University, Ulianovskaya 2, St. Petersburg, 198904, Russia
- MR Author ID: 211673
- Email: korotyaev@gmail.com
- Natalia Saburova
- Affiliation: Department of Mathematical Analysis, Algebra and Geometry, Institute of Mathematics, Information and Space Technologies, Northern (Arctic) Federal University, Uritskogo St. 68, Arkhangelsk, 163002, Russia
- MR Author ID: 1073098
- Email: n.saburova@gmail.com
- Received by editor(s): October 13, 2013
- Received by editor(s) in revised form: May 18, 2014
- Published electronically: March 27, 2015
- Communicated by: Joachim Krieger
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 3951-3967
- MSC (2010): Primary 47A10
- DOI: https://doi.org/10.1090/S0002-9939-2015-12586-5
- MathSciNet review: 3359585