Spectral theory of infinite quantum graphs

Pavel Exner Aleksey Kostenko Mark Malamud Hagen Neidhardt

Combinatorics mathscidoc:1910.43179

Annales Henri Poincar, 19, (11), 3457-3510, 2018.11
We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection between spectral properties of a quantum graph and the corresponding properties of a certain weighted discrete Laplacian on the underlying discrete graph. Using this connection together with spectral theory of (unbounded) discrete Laplacians on infinite graphs, we prove a number of new results on spectral properties of quantum graphs. Namely, we prove several self-adjointness results including a Gaffney-type theorem. We investigate the problem of lower semiboundedness, prove several spectral estimates (bounds for the bottom of spectra and essential spectra of quantum graphs, CLR-type estimates) and study spectral types.
No keywords uploaded!
[ Download ] [ 2019-10-20 13:24:49 uploaded by Pavel_Exner ] [ 653 downloads ] [ 0 comments ]
  title={Spectral theory of infinite quantum graphs},
  author={Pavel Exner, Aleksey Kostenko, Mark Malamud, and Hagen Neidhardt},
  booktitle={Annales Henri Poincar},
Pavel Exner, Aleksey Kostenko, Mark Malamud, and Hagen Neidhardt. Spectral theory of infinite quantum graphs. 2018. Vol. 19. In Annales Henri Poincar. pp.3457-3510. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132449980260708.
Please log in for comment!
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved