INVERSE PROBLEMS FOR QUANTUM TREES II: RECOVERING MATCHING CONDITIONS FOR STAR GRAPHS
2010 (English)In: Inverse Problems and Imaging, ISSN 1930-8337, Vol. 4, no 4, 579-598 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2010. Vol. 4, no 4, 579-598 p.
quantum graphs, inverse problems, matching conditions
IdentifiersURN: urn:nbn:se:su:diva-66232DOI: 10.3934/ipi.2010.4.579ISI: 000282648200003OAI: oai:DiVA.org:su-66232DiVA: diva2:467623
authorCount :32011-12-192011-12-192011-12-19Bibliographically approved