Eigenvalue asymptotics and unique continuation of eigenfunctions on planar graphs
Combinatorics
2021-04-09 v1 Spectral Theory
Abstract
We study planar graphs with large negative curvature outside of a finite set and the spectral theory of Schr{\"o}dinger operators on these graphs. We obtain estimates on the first and second order term of the eigenvalue asymptotics. Moreover, we prove a unique continuation result for eigenfunctions and decay properties of general eigenfunctions. The proofs rely on a detailed analysis of the geometry which employs a Copy-and-Paste procedure based on the Gau{\ss}-Bonnet theorem.
Cite
@article{arxiv.2104.03582,
title = {Eigenvalue asymptotics and unique continuation of eigenfunctions on planar graphs},
author = {Michel Bonnefont and Sylvain Golenia and Matthias Keller},
journal= {arXiv preprint arXiv:2104.03582},
year = {2021}
}