Invariants and spectral estimates for Laplacians on periodic graphs

N. Saburova, E. Korotyaev

Research outputpeer-review

Abstract

We consider Laplacians on periodic discrete graphs. The spectrum of the Laplacian consists of a finite number of bands, where degenerate bands are eigenvalues of infinite multiplicity. We introduce a new invariant I for periodic graphs and obtain a decomposition of the Laplacian into a direct integral, where fiber Laplacians (matrices) have the minimal number (≤ 2I) of coefficients depending on the quasimomentum. Using this decomposition, we estimate the position of each band and the Lebesgue measure of the Laplacian spectrum in terms of the new invariants. Moreover, similar results for Schrödinger operators with periodic potentials are obtained.

Original languageEnglish
Title of host publicationProceedings of the International Conference Days on Diffraction, DD 2018
EditorsA.Ya. Kazakov, A.P. Kiselev, L.I. Goray, O.V. Motygin
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages263-268
Number of pages6
ISBN (Electronic)9781728103136
DOIs
Publication statusPublished - 29 Nov 2018
EventInternational conference Days on Diffraction-2018 - St Petersburg
Duration: 4 Jun 20188 Jun 2018

Publication series

NameProceedings of the International Conference Days on Diffraction, DD 2018

Conference

ConferenceInternational Conference on Days on Diffraction (DD)
CountryRussian Federation
CitySt Petersburg
Period4/06/188/06/18

Scopus subject areas

  • Mechanics of Materials
  • Safety, Risk, Reliability and Quality
  • Computational Mathematics
  • Astronomy and Astrophysics
  • Radiation

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    Saburova, N., & Korotyaev, E. (2018). Invariants and spectral estimates for Laplacians on periodic graphs. In A. Y. Kazakov, A. P. Kiselev, L. I. Goray, & O. V. Motygin (Eds.), Proceedings of the International Conference Days on Diffraction, DD 2018 (pp. 263-268). [8553048] (Proceedings of the International Conference Days on Diffraction, DD 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD.2018.8553048