Inverse Problems for Sturm-Liouville Differential Operators on Closed Sets
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Abstract
Second-order differential operators on closed sets (time scales) are considered. Properties of their spectral characteristics are obtained and inverse problems are studied, which consists in recovering the operators from their spectral characteristics. We establish the uniqueness and develop constructive algorithms for the solution of the inverse problems.
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Yurko, V. (2019). Inverse Problems for Sturm-Liouville Differential Operators on Closed Sets. Tamkang Journal of Mathematics, 50(3), 199–206. https://doi.org/10.5556/j.tkjm.50.2019.3343
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References
1. Bohner, M., Peterson, A. Dynamic Equations on Time Scales. Birkh\"auser, Boston, MA (2001).
2. Bohner, M., Peterson, A. Advances in Dynamic Equations on Time Scales. Birkha\"auser, Boston, MA (2003).
3. Marchenko, V. A. Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977; English transl., Birkh\"auser, 1986.
4.Levitan, B. M. Inverse Sturm-Liouville Problems, Nauka, Moscow, 1984; Engl. transl., VNU Sci.Press, Utrecht, 1987.
5.Freiling, G.; Yurko, V. A. Inverse Sturm-Liouville Problems and Their Applications, NOVA Science Publishers, New York, 2001.
6.Yurko, V. A. Method of Spectral Mappings in the Invers Problem Theory, Inverse and Ill-posed Problems Series, VSP, Utrecht, 2002.
7.Ozkan, S. Ambarzumian-type theorem on a time scale, Journal of Inverse and Ill-Posed Problems (2018)
2. Bohner, M., Peterson, A. Advances in Dynamic Equations on Time Scales. Birkha\"auser, Boston, MA (2003).
3. Marchenko, V. A. Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977; English transl., Birkh\"auser, 1986.
4.Levitan, B. M. Inverse Sturm-Liouville Problems, Nauka, Moscow, 1984; Engl. transl., VNU Sci.Press, Utrecht, 1987.
5.Freiling, G.; Yurko, V. A. Inverse Sturm-Liouville Problems and Their Applications, NOVA Science Publishers, New York, 2001.
6.Yurko, V. A. Method of Spectral Mappings in the Invers Problem Theory, Inverse and Ill-posed Problems Series, VSP, Utrecht, 2002.
7.Ozkan, S. Ambarzumian-type theorem on a time scale, Journal of Inverse and Ill-Posed Problems (2018)