Standard

Estimates of bands for Laplacians on periodic equilateral metric graphs. / Korotyaev, E.; Saburova, N.

In: Proceedings of the American Mathematical Society, Vol. 144, No. No 4, 2016, p. 1605--1617.

Research output: Contribution to journal › Article

Harvard

Korotyaev, E & Saburova, N 2016, 'Estimates of bands for Laplacians on periodic equilateral metric graphs', Proceedings of the American Mathematical Society, vol. 144, no. No 4, pp. 1605--1617. https://doi.org/10.1090/proc/12815

APA

Korotyaev, E., & Saburova, N. (2016). Estimates of bands for Laplacians on periodic equilateral metric graphs. Proceedings of the American Mathematical Society, 144(No 4,), 1605--1617. https://doi.org/10.1090/proc/12815

Vancouver

Korotyaev E, Saburova N. Estimates of bands for Laplacians on periodic equilateral metric graphs. Proceedings of the American Mathematical Society. 2016;144(No 4,):1605--1617. https://doi.org/10.1090/proc/12815

Author

Korotyaev, E. ; Saburova, N. / Estimates of bands for Laplacians on periodic equilateral metric graphs. In: Proceedings of the American Mathematical Society. 2016 ; Vol. 144, No. No 4,. pp. 1605--1617.

BibTeX

@article{f77b11b58cd8425db847538a989e32e7,
title = "Estimates of bands for Laplacians on periodic equilateral metric graphs",
abstract = "Abstract. We consider Laplacians on periodic equilateral metric graphs. The spectrum of the Laplacian consists of an absolutely continuous part (which is a union of an infinite number of non-degenerate spectral bands) plus an infinite number of flat bands, i.e., eigenvalues of infinite multiplicity. We estimate the Lebesgue measure of the bands on a finite interval in terms of geometric parameters of the graph. The proof is based on spectral properties of discrete Laplacians.",
keywords = "Spectral bands, flat bands, Laplace operator, periodic equilateralmetric graph.",
author = "E. Korotyaev and N. Saburova",
year = "2016",
doi = "10.1090/proc/12815",
language = "English",
volume = "144",
pages = "1605----1617",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "No 4,",

}

RIS

TY - JOUR

T1 - Estimates of bands for Laplacians on periodic equilateral metric graphs

AU - Korotyaev, E.

AU - Saburova, N.

PY - 2016

Y1 - 2016

N2 - Abstract. We consider Laplacians on periodic equilateral metric graphs. The spectrum of the Laplacian consists of an absolutely continuous part (which is a union of an infinite number of non-degenerate spectral bands) plus an infinite number of flat bands, i.e., eigenvalues of infinite multiplicity. We estimate the Lebesgue measure of the bands on a finite interval in terms of geometric parameters of the graph. The proof is based on spectral properties of discrete Laplacians.

AB - Abstract. We consider Laplacians on periodic equilateral metric graphs. The spectrum of the Laplacian consists of an absolutely continuous part (which is a union of an infinite number of non-degenerate spectral bands) plus an infinite number of flat bands, i.e., eigenvalues of infinite multiplicity. We estimate the Lebesgue measure of the bands on a finite interval in terms of geometric parameters of the graph. The proof is based on spectral properties of discrete Laplacians.

KW - Spectral bands

KW - flat bands

KW - Laplace operator

KW - periodic equilateralmetric graph.

U2 - 10.1090/proc/12815

DO - 10.1090/proc/12815

M3 - Article

VL - 144

SP - 1605

EP - 1617

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - No 4,

ER -

ID: 7560953