### An inverse problem for the non-self-adjoint matrix Sturm-Liouville operator

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

V. A. Marchenko, Sturm-Liouville Operators and their Applications, Naukova Dumka, Kiev (1977) (Russian); English transl., Birkhauser, 1986.

B. M. Levitan, Inverse Sturm-Liouville Problems, Nauka, Moscow (1984) (Russian); English transl., VNU Sci. Press, Utrecht, 1987.

J. Poschel and E. Trubowitz, Inverse Spectral Theory, New York, Academic Press, 1987.

G. Freiling and V. Yurko, Inverse Sturm-Liouville problems and their applications, Huntington, NY: Nova Science Publishers, 305 p., 2001.

Z. S. Agranovich and V. A. Marchenko, The inverse problem of scattering theory [in Russian], KSU, Kharkov, 1960; Gordon and Breach, New York, 1963 (Eng. Transl.).

R. Carlson, An inverse problem for the matrix Schrodinger equation, J. Math. Anal. Appl., 267(2002), 564--575.

M. M. Malamud, Uniqueness of the matrix Sturm-Liouville equation given a part of the monodromy matrix, and Borg type results, Sturm-Liouville Theory, Birkhauser, Basel, (2005), 237--270.

V. A. Yurko, Inverse problems for matrix Sturm-Liouville operators, Russian J. Math. Phys., 13,no.1 (2006), 111--118.

V. A. Yurko, Inverse problems for the matrix Sturm-Liouville equation on a finite interval, Inverse Problems, 22(2006), 1139--1149.

D. Chelkak and E. Korotyaev, Weyl-Titchmarsh functions of vector-valued Sturm-Liouville operators on the unit interval, J. Func. Anal. 257(2009), 1546--1588.

N. Bondarenko, Spectral analysis for the matrix Sturm-Liouville operator on a finite interval, Tamkang J. Math., 42: 3 (2011), 305--327.

Ya. V. Mykytyuk and N. S. Trush, Inverse spectral problems for Sturm-Liouville operators with matrix-valued potentials, Inverse Problems, 26(2010), 015009.

N. Bondarenko, An inverse spectral problem for the matrix Sturm-Liouville operator on the half-line, Boundary Value Problems. 2015:15.

N. Bondarenko, Inverse scattering on the line for the matrix Sturm-Liouville equation, J. Differential Equations, 262(2017),Issue 3, 2073--2105.

V. A. Yurko, An inverse spectral problem for singular non-self-adjoint differential systems, Sbornik: Mathematics (2004) 195:12, 1823--1854.

V. A. Yurko, Reconstruction of non-self-adjoint differential systems on the half-Line from the Weyl matrix, Mathematical Notes (2004), 76, no.~2, 296--302.

V. A. Yurko, An inverse problem for differential systems on a finite interval in the case of multiple roots of the characteristic polynomial, Diff. Equ., 41(2005), no. 6, 818--823.

V. A. Yurko, Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-Posed Problems Series, Utrecht: VSP, 2002.

S. A. Buterin, On inverse spectral problem for non-selfadjoint Sturm-Liouville operator on a finite interval, Journal of Mathematical Analysis and Applications, 335(2007), Issue 1, 739--749.

S. A. Buterin, C.-T. Shieh, and V. A. Yurko, Inverse spectral problems for non-selfadjoint second-order differential operators with Dirichlet boundary conditions,

Boundary Value Problems (2013), 2013:180, 1--24.

M. A. Naimark, Linear Differential Operators, 2nd ed., Nauka, Moscow (1969); English transl. of 1st ed., Parts I,II, Ungar, New York (1967, 1968).

DOI: http://dx.doi.org/10.5556/j.tkjm.50.2019.2735

Sponsored by Tamkang University | ISSN 0049-2930 (Print), ISSN 2073-9826 (Online) |