On the Inverse Spectral Problems for Quantum Graphs
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We review some aspects of inverse spectral problems for quantum graphs. Under hypothesis of rational independence of lengths of edges it is possible, thanks to trace formulas, to reconstruct information on compact and non compact graphs from the knowledge, respectively, of the spectrum of Laplacian and of the scattering phase. In the case of Sturm-Liouville operators defined on compact graphs and in general for differential operators on compact star-graphs, unknown potentials can be recovered from the knowledge of the spectrum of operators obtained imposing different boundary conditions.
KeywordsInverse problems Inverse scattering problems Sturm-Liouville operators Quantum graphs
MSC 201035R30 81U40 34B24
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