@inproceedings{4be8da533e22460c9f5ec2575b81cdb4,
title = "Inverse Problems for Quantum Trees II: Recovering matching conditions for star graphs",
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.",
keywords = "matching conditions, quantum graphs, inverse problems",
author = "Sergei Avdonin and Pavel Kurasov and Marlena Nowaczyk",
year = "2010",
doi = "10.3934/ipi.2010.4.579",
language = "English",
volume = "4",
publisher = "American Institute of Mathematical Sciences",
number = "4",
pages = "579--598",
booktitle = "Inverse Problems and Imaging",
address = "United States",
note = "International Conference on Integral Geometry and Tomography ; Conference date: 12-08-2008 Through 15-08-2008",
}