Visibility of quantum graph spectrum from the vertices

We investigate the relation between the eigenvalues of the Laplacian with Kirchhoff vertex
conditions on a finite metric graph and a corresponding Titchmarsh–Weyl function (a
parameter-dependent Neumann-to-Dirichlet map). We give a complete description of all real
resonances, including multiplicities, in terms of the edge lengths and the connectivity of the
graph, and apply it to characterize all eigenvalues which are visible for the Titchmarsh–Weyl

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