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.
|Title of host publication||Inverse Problems and Imaging|
|Publisher||American Institute of Mathematical Sciences|
|Publication status||Published - 2010|
|Event||International Conference on Integral Geometry and Tomography - Stockholm, Sweden|
Duration: 2008 Aug 12 → 2008 Aug 15
|Conference||International Conference on Integral Geometry and Tomography|
|Period||2008/08/12 → 2008/08/15|