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

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

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.

Details

Authors
  • Sergei Avdonin
  • Pavel Kurasov
  • Marlena Nowaczyk
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • matching conditions, quantum graphs, inverse problems
Original languageEnglish
Title of host publicationInverse Problems and Imaging
PublisherAmerican Institute of Mathematical Sciences
Pages579-598
Volume4
StatePublished - 2010
Publication categoryResearch
Peer-reviewedYes
EventInternational Conference on Integral Geometry and Tomography - Stockholm, Sweden
Duration: 2008 Aug 122008 Aug 15

Publication series

Name
Number4
Volume4
ISSN (Print)1930-8345
ISSN (Electronic)1930-8337

Conference

ConferenceInternational Conference on Integral Geometry and Tomography
CountrySweden
CityStockholm
Period2008/08/122008/08/15