OPTIMIZATION INVERSE SPECTRAL PROBLEM FOR THE ONE-DIMENSIONAL SCHRODINGER OPERATOR ON THE ENTIRE AXIS

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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 q^ such that the first m eigenvalues of the Schrodinger operator with potential q^ coincided with the given values λk*∈ℝ, k=1, m.

About the authors

V. A. Sadovnichii

Lomonosov Moscow State University

Author for correspondence.
Email: info@rector.msu.ru
Russia

Ya. T. Sultanaev

Akmulla Bashkir State Pedagogical University; Moscow Center for Applied and Fundamental Mathematics

Email: sultanaevyt@gmail.com
Ufa, Russia

N. F. Valeev

Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of RAS

Email: valeevnf@yandex.ru
Russia

References

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  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.

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