Eigenvalue Bracketing for Discrete and Metric Graphs
Articles
Overview
published in
publication date
- December 2008
start page
- 806
end page
- 833
issue
- 2
volume
- 348
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
- 0022-247X
Electronic International Standard Serial Number (EISSN)
- 1096-0813
abstract
- We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using various types of boundary conditions at the vertices of the metric graph. Via an explicit correspondence of the equilateral metric and discrete graph spectrum (also in the "exceptional" values of the metric graph corresponding to the Dirichlet spectrum) we carry over these estimates from the metric graph Laplacian to the discrete case. We apply the results to covering graphs and present examples where the covering graph Laplacians have spectral gaps.