Abstract: A short history of inverse Sturm-Liouville problems on a finite interval, on the axis and on the half-axis. Results of Ambarzumian, Borg, Bargmann, Gelfand and Levitan, Marchenko, M.G. Krein, Faddeev. Connection with the theory of entire functions. Generalizations of the results on inverse problems for the case of compact and non-compact graph domains. Open questions.
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