Geodesic
Necessary and Sufficient Conditions for the Solvability of the Inverse Problem for the Matrix Sturm--Liouville Operator
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 65-70.

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The matrix Sturm–Liouville operator on a finite interval with Dirichlet boundary conditions is studied. Properties of its spectral characteristics and the inverse problem of recovering the operator from these characteristics are investigated. Necessary and sufficient conditions on the spectral data of the operator are obtained. Research is conducted in the general case, with no a priori restrictions on the spectrum. A constructive algorithm for solving the inverse problem is provided.
Keywords: matrix Sturm–Liouville operator, spectral data, inverse spectral problem, necessary and sufficient condition. 
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N. P. Bondarenko. Necessary and Sufficient Conditions for the Solvability of the Inverse Problem for the Matrix Sturm--Liouville Operator. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 65-70. http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a5/

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