Characterization of the spectral data of the Sturm-Liouville operator on a star graph

The report is devoted to the inverse spectral problem, which consists in reconstructing the coefficients of the Sturm-Liouville operator on a star graph from spectral data. The solution of the problem is based on the representation of the operator in matrix form and on the development of the ideas of the spectral mapping method, the most universal method in the theory of inverse spectral problems. Necessary and sufficient conditions for the solvability of the inverse problem are obtained, in other words, a characterization of the spectral data of the operator under consideration is given. The report is based on the results of the article [1] and a number of previous works by the author.
[1] Bondarenko N.P. Spectral data characterization for the Sturm-Liouville operator on the star-shaped graph. Analysis and Mathematical Physics. 2020. 10. № 83.