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Inverse problems for quantum trees

Avdonin, Serguei and Kurasov, Pavel LU (2008) In Inverse Problems and Imaging 2(1). p.1-21
Abstract (Swedish)
Abstract in Undetermined

Three different inverse problems for the Schrodinger operator on a metric tree are considered, so far with standard boundary conditions at the vertices. These inverse problems are connected with the matrix Titchmarsh-Weyl function, response operator ( dynamic Dirichlet-to-Neumann map) and scattering matrix. Our approach is based on the boundary control ( BC) method and in particular on the study of the response operator. It is proven that the response operator determines the quantum tree completely, i.e. its connectivity, lengths of the edges and potentials on them. The same holds if the response operator is known for all but one boundary points, as well as for the Titchmarsh-Weyl function and... (More)
Abstract in Undetermined

Three different inverse problems for the Schrodinger operator on a metric tree are considered, so far with standard boundary conditions at the vertices. These inverse problems are connected with the matrix Titchmarsh-Weyl function, response operator ( dynamic Dirichlet-to-Neumann map) and scattering matrix. Our approach is based on the boundary control ( BC) method and in particular on the study of the response operator. It is proven that the response operator determines the quantum tree completely, i.e. its connectivity, lengths of the edges and potentials on them. The same holds if the response operator is known for all but one boundary points, as well as for the Titchmarsh-Weyl function and scattering matrix. If the connectivity of the graph is known, then the lengths of the edges and the corresponding potentials are determined by just the diagonal terms of the data. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
inverse problems, quantum graphs, Schrodinger equation, wave equation, controllability, boundary control
in
Inverse Problems and Imaging
volume
2
issue
1
pages
1 - 21
publisher
Amer Inst Mathematical Sciences
external identifiers
  • wos:000255217100001
ISSN
1930-8345
language
English
LU publication?
yes
id
9e1fac52-9202-4c85-a4ee-2c14ed01a6db (old id 758116)
date added to LUP
2007-12-27 16:32:28
date last changed
2016-04-15 20:00:38
@article{9e1fac52-9202-4c85-a4ee-2c14ed01a6db,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
Three different inverse problems for the Schrodinger operator on a metric tree are considered, so far with standard boundary conditions at the vertices. These inverse problems are connected with the matrix Titchmarsh-Weyl function, response operator ( dynamic Dirichlet-to-Neumann map) and scattering matrix. Our approach is based on the boundary control ( BC) method and in particular on the study of the response operator. It is proven that the response operator determines the quantum tree completely, i.e. its connectivity, lengths of the edges and potentials on them. The same holds if the response operator is known for all but one boundary points, as well as for the Titchmarsh-Weyl function and scattering matrix. If the connectivity of the graph is known, then the lengths of the edges and the corresponding potentials are determined by just the diagonal terms of the data.},
  author       = {Avdonin, Serguei and Kurasov, Pavel},
  issn         = {1930-8345},
  keyword      = {inverse problems,quantum graphs,Schrodinger equation,wave equation,controllability,boundary control},
  language     = {eng},
  number       = {1},
  pages        = {1--21},
  publisher    = {Amer Inst Mathematical Sciences},
  series       = {Inverse Problems and Imaging},
  title        = {Inverse problems for quantum trees},
  volume       = {2},
  year         = {2008},
}