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Inverse Problems for Quantum Trees II: Recovering matching conditions for star graphs

Avdonin, Sergei; Kurasov, Pavel LU and Nowaczyk, Marlena (2010) International Conference on Integral Geometry and Tomography In Inverse Problems and Imaging 4(4). p.579-598
Abstract
The inverse problem for the Schrodinger operator on a star graph is investigated. It is proven that such Schrodinger operator, i.e. the graph, the real potential on it and the matching conditions at the central vertex, can be reconstructed from the Titchmarsh-Weyl matrix function associated with the graph boundary. The reconstruction is also unique if the spectral data include not the whole Titchmarsh-Weyl function but its principal block (the matrix reduced by one dimension). The same result holds true if instead of the Titchmarsh-Weyl function the dynamical response operator or just its principal block is known.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
matching conditions, quantum graphs, inverse problems
in
Inverse Problems and Imaging
volume
4
issue
4
pages
579 - 598
publisher
American Institute of Mathematical Sciences
conference name
International Conference on Integral Geometry and Tomography
external identifiers
  • wos:000282648200003
  • scopus:78149309499
ISSN
1930-8337
1930-8345
DOI
10.3934/ipi.2010.4.579
language
English
LU publication?
yes
id
4be8da53-3e22-460c-9f5e-c2575b81cdb4 (old id 1720505)
date added to LUP
2010-12-09 13:13:14
date last changed
2018-06-10 03:00:17
@inproceedings{4be8da53-3e22-460c-9f5e-c2575b81cdb4,
  abstract     = {The inverse problem for the Schrodinger operator on a star graph is investigated. It is proven that such Schrodinger operator, i.e. the graph, the real potential on it and the matching conditions at the central vertex, can be reconstructed from the Titchmarsh-Weyl matrix function associated with the graph boundary. The reconstruction is also unique if the spectral data include not the whole Titchmarsh-Weyl function but its principal block (the matrix reduced by one dimension). The same result holds true if instead of the Titchmarsh-Weyl function the dynamical response operator or just its principal block is known.},
  author       = {Avdonin, Sergei and Kurasov, Pavel and Nowaczyk, Marlena},
  booktitle    = {Inverse Problems and Imaging},
  issn         = {1930-8337},
  keyword      = {matching conditions,quantum graphs,inverse problems},
  language     = {eng},
  number       = {4},
  pages        = {579--598},
  publisher    = {American Institute of Mathematical Sciences},
  title        = {Inverse Problems for Quantum Trees II: Recovering matching conditions for star graphs},
  url          = {http://dx.doi.org/10.3934/ipi.2010.4.579},
  volume       = {4},
  year         = {2010},
}