Geodesic
The inverse problem of spectral analysis for the matrix Sturm--Liouville equation
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 4, pp. 3-13

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The inverse spectral problem is investigated for the matrix Sturm–Liouville equation on a finite interval. The article provides properties of spectral characteristics, a constructive procedure for the solution of the inverse problem along with necessary and sufficient conditions for its solvability has been obtained. 
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     author = {N. P. Bondarenko},
     title = {The inverse problem of spectral analysis for the matrix {Sturm--Liouville} equation},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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N. P. Bondarenko. The inverse problem of spectral analysis for the matrix Sturm--Liouville equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 4, pp. 3-13. http://geodesic.mathdoc.fr/item/ISU_2010_10_4_a0/