Visibility of quantum graph spectrum from the vertices

Publikationstyp
Journal Article
Date Issued
2018-02-06
Sprache
English
Author(s)
Kühn, Christian  
Rohleder, Jonathan  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/3124
Journal
Journal of Physics A: Mathematical and Theoretical  
Volume
51
Issue
9
Article Number
095204
Citation
Journal of Physics A: Mathematical and Theoretical 9 (51): 095204 (2018-02-06)
Publisher DOI
10.1088/1751-8121/aaa884
Scopus ID
2-s2.0-85041912374
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.