- PII
- 10.31857/S0374064124040043-1
- DOI
- 10.31857/S0374064124040043
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 60 / Issue number 4
- Pages
- 492-499
- Abstract
- We investigate the statement of the optimization inverse spectral problem with incomplete spectral data for the one-dimensional Schr¨odinger operator on the entire axis: for a given potential q0, find the closest function such that the first m eigenvalues of the Schrodinger operator with potential coincided with the given values .
- Keywords
- обратная спектральная задача система нелинейных уравнений Шрёдингера оператор Шрёдингера
- Date of publication
- 19.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 9
References
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- 2. Chu, M. Inverse Eigenvalue Problems: Theory, Algorithms, and Applications / M. Chu, G.H. Golub. — Oxford : Oxford University Press, 2005. — 387 p.
- 3. Ilyasov, Y.Sh. On nonlinear boundary value problem corresponding to ???? -dimensional inverse spectral problem / Y.Sh. Ilyasov, N.F. Valeev // J. Differ. Equat. — 2019. — V. 266, № 8. — P. 4533–4543.
- 4. Ilyasov, Ya. Recovery of the nearest potential field from the ???? observed eigenvalues / Ya. Ilyasov, N. Valeev // Physica D: Nonlinear Phenomena. — 2021. — V. 426, № 5. — Art. 132985.
- 5. Tian, Y. On the polynomial integrability of the critical systems for optimal eigenvalue gaps / Y. Tian, Q. Wei, and M. Zhang // J. Math. Phys. — 2023. — V. 64. — Art. 092701.
- 6. Zhao, M. Optimal inverse problems of potentials for two given eigenvalues of Sturm–Liouville problems / M. Zhao, J. Qi // Proc. of the Royal Society of Edinburgh: Section A Mathematics. Published online. — 2024. — 24 p.
- 7. Wei, Q. Extremal values of eigenvalues of Sturm–Liouville operators with potentials in ????1 balls / Q. Wei, G. Meng, M. Zhang // J. Differ. Equat. — 2009. — V. 247, № 2. — P. 364–400.
- 8. Садовничий, В.А. Оптимизационная спектральная задача для оператора Штурма–Лиувилля в пространстве вектор-функций / В.А. Садовничий, Я.Т. Султанаев, Н.Ф. Валеев // Докл. РАН. Математика, информатика, процессы управления. — 2023. — Т. 513. — С. 93–98.
- 9. Садовничий, В.А. Оптимизационная обратная спектральная задача для векторного оператора Штурма–Лиувилля / В.А. Садовничий, Я.Т. Султанаев, Н.Ф. Валеев // Дифференц. уравнения. — 2022. — T. 58, № 12. — С. 1707–1711.
- 10. Yurko, V.A., Inverse Spectral Problems and their Applications, Saratov: PI Press, 2001.
- 11. Chu, M. and Golub, G.H., Inverse Eigenvalue Problems: Theory, Algorithms, and Applications, Oxford: Oxford University Press, 2005.
- 12. Ilyasov, Y.Sh. and Valeev, N.F., On nonlinear boundary value problem corresponding to ???? -dimensional inverse spectral problem, J. Differ. Equat., 2019, vol. 266, no. 8, pp. 4533–4543.
- 13. Ilyasov, Ya. and Valeev, N., Recovery of the nearest potential field from the ???? observed eigenvalues, Physica D: Nonlinear Phenomena, 2021, vol. 426, no. 5, Art. 132985.
- 14. Tian, Y., Wei, Q., and Zhang, M., On the polynomial integrability of the critical systems for optimal eigenvalue gaps, J. Math. Phys., 2023, vol. 64, Art. 092701.
- 15. Zhao, M. and Qi, J., Optimal inverse problems of potentials for two given eigenvalues of Sturm–Liouville problems, Proc. of the Royal Society of Edinburgh: Section A Mathematics, Published online, 2024, pp. 1–24.
- 16. Wei, Q., Meng, G., and Zhang, M., Extremal values of eigenvalues of Sturm–Liouville operators with potentials in ????1 balls, J. Differ. Equat., 2009, vol. 247, no. 2, pp. 364–400.
- 17. Sadovnichii, V.A., Sultanaev, Y.T., and Valeev, N.F., Optimization spectral problem for the Sturm–Liouville operator in a vector function space, Dokl. Math., 2023, vol. 108, pp. 406–410.
- 18. Sadovnichii, V.A., Sultanaev, Y.T., and Valeev, N.F. Optimization inverse spectral problem for a vector Sturm– Liouville operator, Differ. Equat., 2022, vol. 58, pp. 1694–1699.
