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Spectrum of Laplacians on periodic graphs with guides. / Korotyaev, E.; Сабурова, Наталья.

Proceedings of the International Conference Days on Diffraction 2017, DD 2017. ed. / A.P. Kiselev; A.Ya. Kazakov; O.V. Motygin; L.I. Goray; T.A. Suslina; A.S. Kirpichnikova. Vol. 2017-December Institute of Electrical and Electronics Engineers Inc., 2017. p. 282-287.

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

Harvard

Korotyaev, E & Сабурова, Н 2017, Spectrum of Laplacians on periodic graphs with guides. in AP Kiselev, AY Kazakov, OV Motygin, LI Goray, TA Suslina & AS Kirpichnikova (eds), Proceedings of the International Conference Days on Diffraction 2017, DD 2017. vol. 2017-December, Institute of Electrical and Electronics Engineers Inc., pp. 282-287, 2017 International Conference Days on Diffraction, DD 2017, St. Petersburg, Russian Federation, 18/06/17. https://doi.org/10.1109/DD.2017.8168040

APA

Korotyaev, E., & Сабурова, Н. (2017). Spectrum of Laplacians on periodic graphs with guides. In A. P. Kiselev, A. Y. Kazakov, O. V. Motygin, L. I. Goray, T. A. Suslina, & A. S. Kirpichnikova (Eds.), Proceedings of the International Conference Days on Diffraction 2017, DD 2017 (Vol. 2017-December, pp. 282-287). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD.2017.8168040

Vancouver

Korotyaev E, Сабурова Н. Spectrum of Laplacians on periodic graphs with guides. In Kiselev AP, Kazakov AY, Motygin OV, Goray LI, Suslina TA, Kirpichnikova AS, editors, Proceedings of the International Conference Days on Diffraction 2017, DD 2017. Vol. 2017-December. Institute of Electrical and Electronics Engineers Inc. 2017. p. 282-287 https://doi.org/10.1109/DD.2017.8168040

Author

Korotyaev, E. ; Сабурова, Наталья. / Spectrum of Laplacians on periodic graphs with guides. Proceedings of the International Conference Days on Diffraction 2017, DD 2017. editor / A.P. Kiselev ; A.Ya. Kazakov ; O.V. Motygin ; L.I. Goray ; T.A. Suslina ; A.S. Kirpichnikova. Vol. 2017-December Institute of Electrical and Electronics Engineers Inc., 2017. pp. 282-287

BibTeX

@inproceedings{415fcf1a02b44ae3bb9939bdfff5ece8,
title = "Spectrum of Laplacians on periodic graphs with guides",
abstract = "We consider Laplace operators on periodic discrete graphs perturbed by guides, i.e., graphs which are periodic in some directions and finite in other ones. We show that the spectrum of the Laplacian on the perturbed graph consists of the spectrum of the Laplacian on the unperturbed periodic graph and the additional so-called guided spectrum which is a union of a finite number of bands. We estimate the position of the guided bands and their length in terms of geometric parameters of the graph. We also determine the asymptotics of the guided bands for guides with large multiplicity of edges.",
author = "E. Korotyaev and Наталья Сабурова",
year = "2017",
month = dec,
day = "5",
doi = "10.1109/DD.2017.8168040",
language = "English",
volume = "2017-December",
pages = "282--287",
editor = "A.P. Kiselev and A.Ya. Kazakov and O.V. Motygin and L.I. Goray and T.A. Suslina and A.S. Kirpichnikova",
booktitle = "Proceedings of the International Conference Days on Diffraction 2017, DD 2017",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "United States",
note = "2017 International Conference Days on Diffraction, DD 2017 ; Conference date: 18-06-2017 Through 22-06-2017",

}

RIS

TY - GEN

T1 - Spectrum of Laplacians on periodic graphs with guides

AU - Korotyaev, E.

AU - Сабурова, Наталья

PY - 2017/12/5

Y1 - 2017/12/5

N2 - We consider Laplace operators on periodic discrete graphs perturbed by guides, i.e., graphs which are periodic in some directions and finite in other ones. We show that the spectrum of the Laplacian on the perturbed graph consists of the spectrum of the Laplacian on the unperturbed periodic graph and the additional so-called guided spectrum which is a union of a finite number of bands. We estimate the position of the guided bands and their length in terms of geometric parameters of the graph. We also determine the asymptotics of the guided bands for guides with large multiplicity of edges.

AB - We consider Laplace operators on periodic discrete graphs perturbed by guides, i.e., graphs which are periodic in some directions and finite in other ones. We show that the spectrum of the Laplacian on the perturbed graph consists of the spectrum of the Laplacian on the unperturbed periodic graph and the additional so-called guided spectrum which is a union of a finite number of bands. We estimate the position of the guided bands and their length in terms of geometric parameters of the graph. We also determine the asymptotics of the guided bands for guides with large multiplicity of edges.

UR - http://www.scopus.com/inward/record.url?scp=85045983316&partnerID=8YFLogxK

U2 - 10.1109/DD.2017.8168040

DO - 10.1109/DD.2017.8168040

M3 - Conference contribution

AN - SCOPUS:85045983316

VL - 2017-December

SP - 282

EP - 287

BT - Proceedings of the International Conference Days on Diffraction 2017, DD 2017

A2 - Kiselev, A.P.

A2 - Kazakov, A.Ya.

A2 - Motygin, O.V.

A2 - Goray, L.I.

A2 - Suslina, T.A.

A2 - Kirpichnikova, A.S.

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 International Conference Days on Diffraction, DD 2017

Y2 - 18 June 2017 through 22 June 2017

ER -

ID: 35631678