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Schrödinger operators on graphs and geometry I: Essentially bounded potentials

Kurasov, Pavel LU (2008) In Journal of Functional Analysis 254(4). p.934-953
Abstract
The inverse spectral problem for Schrödinger operators on finite compact metric graphs is investigated. The relations between the spectral asymptotics and geometric properties of the underlying graph are studied. It is proven that the Euler characteristic of the graph can be calculated from the spectrum of the Schrödinger operator in the case of essentially bounded real potentials and standard boundary conditions at the vertices. Several generalizations of the presented results are discussed.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Quantum, graph, Trace formula, Euler characteristic
in
Journal of Functional Analysis
volume
254
issue
4
pages
934 - 953
publisher
Elsevier
external identifiers
  • wos:000253175800003
  • scopus:38049083801
ISSN
0022-1236
DOI
10.1016/j.jfa.2007.11.007
language
English
LU publication?
yes
id
97ef79d7-6057-4f45-968d-6241f88af76c (old id 758118)
alternative location
http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WJJ-4RD3WMH-1-1&_cdi=6880&_user=745831&_orig=search&_coverDate=02%2F15%2F2008&_sk=997459995&view=c&wchp=dGLbVzz-zSkWb&md5=d08c4e45582837cfe4e15eedba821627&ie=/sdarticle.pdf
date added to LUP
2008-03-04 14:25:25
date last changed
2017-09-10 04:06:42
@article{97ef79d7-6057-4f45-968d-6241f88af76c,
  abstract     = {The inverse spectral problem for Schrödinger operators on finite compact metric graphs is investigated. The relations between the spectral asymptotics and geometric properties of the underlying graph are studied. It is proven that the Euler characteristic of the graph can be calculated from the spectrum of the Schrödinger operator in the case of essentially bounded real potentials and standard boundary conditions at the vertices. Several generalizations of the presented results are discussed.},
  author       = {Kurasov, Pavel},
  issn         = {0022-1236},
  keyword      = {Quantum,graph,Trace formula,Euler characteristic},
  language     = {eng},
  number       = {4},
  pages        = {934--953},
  publisher    = {Elsevier},
  series       = {Journal of Functional Analysis},
  title        = {Schrödinger operators on graphs and geometry I: Essentially bounded potentials},
  url          = {http://dx.doi.org/10.1016/j.jfa.2007.11.007},
  volume       = {254},
  year         = {2008},
}