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Invariants and spectral estimates for Laplacians on periodic graphs. / Saburova, N.; Korotyaev, E.

Proceedings of the International Conference Days on Diffraction, DD 2018. ed. / A.Ya. Kazakov; A.P. Kiselev; L.I. Goray; O.V. Motygin. Institute of Electrical and Electronics Engineers Inc., 2018. p. 263-268 8553048 (Proceedings of the International Conference Days on Diffraction, DD 2018).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Saburova, N & Korotyaev, E 2018, Invariants and spectral estimates for Laplacians on periodic graphs. in AY Kazakov, AP Kiselev, LI Goray & OV Motygin (eds), Proceedings of the International Conference Days on Diffraction, DD 2018., 8553048, Proceedings of the International Conference Days on Diffraction, DD 2018, Institute of Electrical and Electronics Engineers Inc., pp. 263-268, 2018 International Conference Days on Diffraction, DD 2018, St. Petersburg, Russian Federation, 4/06/18. https://doi.org/10.1109/DD.2018.8553048

APA

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

Vancouver

Saburova N, Korotyaev E. Invariants and spectral estimates for Laplacians on periodic graphs. In Kazakov AY, Kiselev AP, Goray LI, Motygin OV, editors, Proceedings of the International Conference Days on Diffraction, DD 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 263-268. 8553048. (Proceedings of the International Conference Days on Diffraction, DD 2018). https://doi.org/10.1109/DD.2018.8553048

Author

Saburova, N. ; Korotyaev, E. / Invariants and spectral estimates for Laplacians on periodic graphs. Proceedings of the International Conference Days on Diffraction, DD 2018. editor / A.Ya. Kazakov ; A.P. Kiselev ; L.I. Goray ; O.V. Motygin. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 263-268 (Proceedings of the International Conference Days on Diffraction, DD 2018).

BibTeX

@inproceedings{4c81c09d28f14a65a84a4ee64c010a0b,
title = "Invariants and spectral estimates for Laplacians on periodic graphs",
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 Schr{\"o}dinger operators with periodic potentials are obtained.",
author = "N. Saburova and E. Korotyaev",
year = "2018",
month = nov,
day = "29",
doi = "10.1109/DD.2018.8553048",
language = "English",
series = "Proceedings of the International Conference Days on Diffraction, DD 2018",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "263--268",
editor = "A.Ya. Kazakov and A.P. Kiselev and L.I. Goray and O.V. Motygin",
booktitle = "Proceedings of the International Conference Days on Diffraction, DD 2018",
address = "United States",
note = "2018 International Conference Days on Diffraction, DD 2018 ; Conference date: 04-06-2018 Through 08-06-2018",

}

RIS

TY - GEN

T1 - Invariants and spectral estimates for Laplacians on periodic graphs

AU - Saburova, N.

AU - Korotyaev, E.

PY - 2018/11/29

Y1 - 2018/11/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85060021952&partnerID=8YFLogxK

U2 - 10.1109/DD.2018.8553048

DO - 10.1109/DD.2018.8553048

M3 - Conference contribution

AN - SCOPUS:85060021952

T3 - Proceedings of the International Conference Days on Diffraction, DD 2018

SP - 263

EP - 268

BT - Proceedings of the International Conference Days on Diffraction, DD 2018

A2 - Kazakov, A.Ya.

A2 - Kiselev, A.P.

A2 - Goray, L.I.

A2 - Motygin, O.V.

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 International Conference Days on Diffraction, DD 2018

Y2 - 4 June 2018 through 8 June 2018

ER -

ID: 46131117