Geodesic
Global solvability of the inverse spectral problem for differential systems on a finite interval
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 2, pp. 200-208.

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The inverse spectral problem is studied for non-selfadjoint systems of ordinary differential equations on a finite interval. We provide necessary and sufficient conditions for the global solvability of the inverse problem, along with an algorithm for constructing its solution. For solving this nonlinear inverse problem, we develop ideas of the method of spectral mappings, which allows one to construct the potential matrix from the given spectral characteristics and establish conditions for the global solvability of the inverse problem considered. 
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V. A. Yurko. Global solvability of the inverse spectral problem for differential systems on a finite interval. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 2, pp. 200-208. http://geodesic.mathdoc.fr/item/ISU_2024_24_2_a4/

[1] Nauka, M., 1988 | DOI | MR | Zbl

[2] Freiling G., Yurko V. A., Inverse Sturm – Liouville Problems and Their Applications, NOVA Science Publishers, New York, 2001, 305 pp. | MR | Zbl

[3] Shabat A. B., “An inverse scattering problem”, Differential Equations, 15:10 (1979), 1299–1307 | MR

[4] Malamud M. M., “Questions of uniqueness in inverse problems for systems of differential equations on a finite interval”, Transactions of the Moscow Mathematical Society, 60 (1999), 173–224 | MR | Zbl

[5] Sakhnovich L. A., Spectral Theory of Canonical Differential Systems. Method of Operator Identities, Operator Theory: Advances and Applications, 107, Birkhauser Verlag, Basel, 1999, 202 pp. | DOI | MR | Zbl

[6] Yurko V. A., Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-Posed Problems Series, 31, VSP, Utrecht, 2002, 303 pp. | DOI | MR

[7] Yurko V. A., “An inverse spectral problem for singular non-selfadjoint differential systems”, Sbornik: Mathematics, 195:12 (2004), 1823–1854 | DOI | MR | Zbl

[8] Yurko V. A., “Inverse spectral problems for differential systems on a finite interval”, Results in Mathematics, 48 (2005), 371–386 | DOI | MR | Zbl

[9] Yurko V. A., “Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix”, Mathematics of the USSR-Sbornik, 72:2 (1992), 413–438 | DOI | MR | Zbl

[10] Yurko V. A., Inverse Spectral Problems for Differential Operators and their Applications, Gordon and Breach, Amsterdam, 2000, 272 pp. | DOI | MR | Zbl