Abstract
The Sturm–Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the remaining edge from the part of the spectrum. A constructive method is developed for the solution of this problem, based on the Riesz-basicity of some sequence of vector functions. The local solvability of the inverse problem and the stability of its solution are proved.
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Acknowledgements
This work was supported in part by the President grant MK-686.2017.1, by Grant 1.1660.2017/PCh of the Russian Ministry of Education and Science and by Grants 15-01-04864, 16-01-00015, 17-51-53180 of the Russian Foundation for Basic Research.
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Bondarenko, N.P. A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph. Anal.Math.Phys. 8, 155–168 (2018). https://doi.org/10.1007/s13324-017-0172-x
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DOI: https://doi.org/10.1007/s13324-017-0172-x
Keywords
- Partial inverse problem
- Differential operator on graph
- Sturm–Liouville operator
- Weyl function
- Riesz basis
- Local solvability
- Stability