Visibility of quantum graph spectrum from the vertices
Spectral Theory
2018-01-19 v3 Mathematical Physics
math.MP
Abstract
We investigate the relation between the eigenvalues of the Laplacian with Kirchhoff vertex conditions on a finite metric graph and a corresponding Titchmarsh-Weyl function (a parameter-dependent Neumann-to-Dirichlet map). We give a complete description of all real resonances, including multiplicities, in terms of the edge lengths and the connectivity of the graph, and apply it to characterize all eigenvalues which are visible for the Titchmarsh-Weyl function.
Cite
@article{arxiv.1602.03394,
title = {Visibility of quantum graph spectrum from the vertices},
author = {Christian Kühn and Jonathan Rohleder},
journal= {arXiv preprint arXiv:1602.03394},
year = {2018}
}
Comments
Substantially revised version; accepted for publication in J. Phys. A: Math. Theor