Abstract
Inverse spectral problems are studied for non-selfadjoint systems of ordinary differential equations on a finite interval. We establish properties of the spectral characteristics, and provide a procedure for constructing the solution of the inverse problem of recovering the coefficients of differential systems from the given spectral characteristics.
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Yurko V.A. Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix. Mat. Sbornik, 182, no.3 (1991), 431–456 (Russian); English transl. in Math. USSR Sbornik, 72, no.2 (1992), 413-438.
Yurko V.A. Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-posed Problems Series. VSP. Utrecht, 2002.
Yurko V.A. Inverse Spectral Problems for Differential Operators and their Applications. Gordon and Breach. Amsterdam; 2000.
Yurko V.A. Inverse Spectral Problems and their Applications, Saratov, PI Press, 2001.
Levitan B.M. and Sargsjan I.S. Sturm-Liouville and Dirac Operators, Nauka, Moscow, 1988; English transl.: Kluwer Academic Publishers, Dordrecht, 1991.
Marchenko V.A. Sturm-Liouville Operators and their Applications, Naukova Dumka, Kiev, 1977; English transl., Birkhauser, 1986.
Levitan B.M. Inverse Sturm-Liouville Problems, Nauka, Moscow, 1984; English transl: VNU Sci.Press, Utrecht, 1987.
Freiling G. and Yurko V.A. Inverse Sturm-Liouville Problems and their Applications. NOVA Science Publishers. New York, 2001.
Shabat A.B. An inverse scattering problem. Differ. Uravneniya 15 (1979), no. 10, 1824–1834; English transl. in Differ. Equations 15 (1979), no. 10, 1299-1307.
Yurko V.A. An inverse problem for systems of differential equations with nonlinear dependence on the spectral parameter. Differ. Uravn. 33, no.3 (1997), 390–395 (in Russian); English transl. in Diff. Equations, 33, no.3 (1997), 388-394.
Malamud M.M. Questions of uniqueness in inverse problems for systems of differential equations on a finite interval. Trudy Mosk. Matem. Obstch. 60 (1999), 199–258; translation in Trans. Moscow Math. Soc. 1999, 173-224.
Sakhnovich L.A. Spectral theory of canonical differential systems. Method of operator identities. Translated from the Russian. Operator Theory: Advances and Appl., 107. Birkhauser Verlag, Basel, 1999.
Beats R., Coifman R.R. Scattering and inverse scattering for first order systems. Comm. Pure Appl. Math. 37 (1984), 39–90.
Yurko V.A. An inverse spectral problem for singular non-selfadjoint differential systems. Mat. Sbornik 195, no. 12 (2004), 123–156 (Russian); English transl. in Sbornik: Mathematics 195, no. 12 (2004), 1823-1854.
Yurko V.A. An inverse problem for differential systems on a finite interval in the case of multiple roots of the characteristic polynomial. Differ. Uravn. 41, no.6 (2005), 781–786; English transl. in Diff. Equations 41, no.6 (2005), 818-823.
Tamarkin Y.D. On Some Problems of Theory of Ordinary Linear Differential Equations, Petrograd, 1917.
Rasulov M.L. Methods of Contour Integration, Amsterdam, North-Holland, 1967.
Vagabov A.I. On sharpening an asymptotic theorem of Tamarkin. Differ. Uravn. 29 (1993), no.1, 41–49; English transl. in Diff. Equations 29 (1993), no.1, 33-41.
Rykhlov V.S. Asymptotical formulas for solutions of linear differential systems of the first order. Results Math. 36 (1999), no. 3–4, 342–353.
Bellmann R. and Cooke K. Differential-difference Equations, Academic Press, New York, 1963.
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Yurko, V. Inverse spectral problems for differential systems on a finite interval. Results. Math. 48, 371–386 (2005). https://doi.org/10.1007/BF03323374
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DOI: https://doi.org/10.1007/BF03323374