Spectral band bracketing for Laplacians on periodic metric graphs
Spectral Theory
2014-07-01 v1
Abstract
We consider Laplacians on periodic metric graphs with unit-length edges. The spectrum of these operators consists of an absolutely continuous part (which is a union of an infinite number of non-degenerated spectral bands) plus an infinite number of flat bands, i.e., eigenvalues of infinite multiplicity. Our main result is a localization of spectral bands in terms of eigenvalues of Dirichlet and Neumann operators on a fundamental domain of the periodic graph. The proof is based on the spectral band localization for discrete Laplacians and on the relation between the spectra of discrete and metric Laplacians.
Keywords
Cite
@article{arxiv.1406.7523,
title = {Spectral band bracketing for Laplacians on periodic metric graphs},
author = {Evgeny Korotyaev and Natalia Saburova},
journal= {arXiv preprint arXiv:1406.7523},
year = {2014}
}
Comments
18 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1310.3461, arXiv:1312.6510