Inverse spectral problem for quantum graphs

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Graph Laplacians and topology (2008, methodology): “We here present formal calculations which are valid in the distributional sense (for details see [19])”
Homogeneous trees of second order Sturm-Liouville equations: A general theory and program (2008, background): “See also [17, 18, 45, 97, 152, 187, 214] for the control theory approach and other discussions of the inverse problem.”
Schrödinger operators on graphs and geometry I: Essentially bounded potentials (2008, unknown): “Let kn and k0n be two real sequences satisfying the following conditions ∣∣kn − k0n∣∣ = O ( 1 n ) , k0n = π Ln + O(1), (19) and the limit limt→∞ ∑∞ n=1 cosk0n/t ( sin k0n/2t k0n/2t )2 exists.”