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Laplacians on periodic graphs with guides. / Korotyaev, Evgeny; Сабурова, Наталья.

In: Journal of Mathematical Analysis and Applications, Vol. 455, No. 2, 15.11.2017, p. 1444-1469.

Research output: Contribution to journal › Article › peer-review

Harvard

Korotyaev, E & Сабурова, Н 2017, 'Laplacians on periodic graphs with guides', Journal of Mathematical Analysis and Applications, vol. 455, no. 2, pp. 1444-1469. https://doi.org/10.1016/j.jmaa.2017.06.039

APA

Korotyaev, E., & Сабурова, Н. (2017). Laplacians on periodic graphs with guides. Journal of Mathematical Analysis and Applications, 455(2), 1444-1469. https://doi.org/10.1016/j.jmaa.2017.06.039

Vancouver

Korotyaev E, Сабурова Н. Laplacians on periodic graphs with guides. Journal of Mathematical Analysis and Applications. 2017 Nov 15;455(2):1444-1469. https://doi.org/10.1016/j.jmaa.2017.06.039

Author

Korotyaev, Evgeny ; Сабурова, Наталья. / Laplacians on periodic graphs with guides. In: Journal of Mathematical Analysis and Applications. 2017 ; Vol. 455, No. 2. pp. 1444-1469.

BibTeX

@article{16f970e6b4af49afa8715557762876bb,
title = "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. The spectrum of the Laplacian on the unperturbed graph is a union of a finite number of non-degenerate bands and eigenvalues of infinite multiplicity. We show that the spectrum of the perturbed Laplacian consists of the unperturbed one plus 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. Moreover, we show that the possible number of guided bands, their length and position can be rather arbitrary for some specific periodic graphs with guides.",
keywords = "Discrete Laplace operator, Guided waves, Periodic graph",
author = "Evgeny Korotyaev and Наталья Сабурова",
year = "2017",
month = nov,
day = "15",
doi = "10.1016/j.jmaa.2017.06.039",
language = "English",
volume = "455",
pages = "1444--1469",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - Laplacians on periodic graphs with guides

AU - Korotyaev, Evgeny

AU - Сабурова, Наталья

PY - 2017/11/15

Y1 - 2017/11/15

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. The spectrum of the Laplacian on the unperturbed graph is a union of a finite number of non-degenerate bands and eigenvalues of infinite multiplicity. We show that the spectrum of the perturbed Laplacian consists of the unperturbed one plus 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. Moreover, we show that the possible number of guided bands, their length and position can be rather arbitrary for some specific periodic graphs with guides.

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. The spectrum of the Laplacian on the unperturbed graph is a union of a finite number of non-degenerate bands and eigenvalues of infinite multiplicity. We show that the spectrum of the perturbed Laplacian consists of the unperturbed one plus 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. Moreover, we show that the possible number of guided bands, their length and position can be rather arbitrary for some specific periodic graphs with guides.

KW - Discrete Laplace operator

KW - Guided waves

KW - Periodic graph

UR - http://www.scopus.com/inward/record.url?scp=85021284229&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2017.06.039

DO - 10.1016/j.jmaa.2017.06.039

M3 - Article

AN - SCOPUS:85021284229

VL - 455

SP - 1444

EP - 1469

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -

ID: 35631528