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Partial Inverse Sturm-Liouville Problems

Author

Listed:
  • Natalia P. Bondarenko

    (Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia
    Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, Samara 443086, Russia
    S.M. Nikolskii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow 117198, Russia)

Abstract

This paper presents a review of both classical and modern results pertaining to partial inverse spectral problems for differential operators. Such problems consist in the recovery of differential expression coefficients in some part of the domain (a finite interval or a geometric graph) from spectral characteristics, while the coefficients in the remaining part of the domain are known a priori. Usually, partial inverse problems require less spectral data than complete inverse problems. In this review, we pay considerable attention to partial inverse problems on graphs and to the unified approach based on the reduction of partial inverse problems to Sturm-Liouville problems with entire analytic functions in a boundary condition. We not only describe the results of selected studies but also compare them with each other and establish interconnections.

Suggested Citation

  • Natalia P. Bondarenko, 2023. "Partial Inverse Sturm-Liouville Problems," Mathematics, MDPI, vol. 11(10), pages 1-44, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2408-:d:1153140
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    References listed on IDEAS

    as
    1. Buterin, S.A. & Malyugina, M.A. & Shieh, C.-T., 2021. "An inverse spectral problem for second-order functional-differential pencils with two delays," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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    1. Sergey Buterin, 2023. "On Recovering Sturm–Liouville-Type Operators with Global Delay on Graphs from Two Spectra," Mathematics, MDPI, vol. 11(12), pages 1-12, June.

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