Inverse spectral problems for Sturm–Liouville operators on graphs

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How researchers see this paper

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Schrödinger operators on graphs and geometry I: Essentially bounded potentials (2008, background): “It is possible to state that this problem is fully understood now [1,3,4,9,27,34,36,37].”
Graph Laplacians and topology (2008, background): “It has been proven by different authors that in the case of finite metric trees, the graphs and the potentials can be reconstructed from the corresponding scattering matrix or certain spectral data [1], [2], [7] and [ 29 ].”
Inverse spectral problems for differential operators on arbitrary compact graphs (2010, methodology): “For solving the inverse problem we develop ideas of the method of spectral mappings [12] and ideas from [4, 11].”
A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph (2017, methodology): “We considered the SturmLiouville operator on the tree, and showed that if the potential is given on one edge, then we need one spectrum less to recover the potential on the whole graph, comparing with the full inverse problem (for example, [10]).”