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On Inverse Spectral Problems for Sturm–Liouville Differential Operators on Closed Sets

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Abstract

We study Sturm–Liouville operators on closed sets of a special structure, which are sometimes referred to as time scales and often appear in modelling various real-world processes. Depending on the set structure, such operators unify both differential and difference operators. The time scales under consideration consist of a finite number of non-intersecting segments. We obtain properties of the spectral characteristics and prove uniqueness theorems for inverse problems of recovering the operator from two types of spectral data: the Weyl function, as well as the spectra of two boundary value problems for one and the same Sturm–Liouville equation on the time scale with one common boundary condition.

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Funding

This work was supported in part by grant 1.1660.2017/4.6 of the Ministry of Education and Science of the Russian Federation and by grant 19-01-00102 of Russian Foundation for Basic Research.

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Authors and Affiliations

  1. Department of Mathematics, Saratov State University, 410012, Saratov, Russia

    M. A. Kuznetsova, S. A. Buterin & V. A. Yurko

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  1. M. A. Kuznetsova
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  2. S. A. Buterin
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  3. V. A. Yurko
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Correspondence to M. A. Kuznetsova, S. A. Buterin or V. A. Yurko.

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(Submitted by A. B. Muravnik)

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Kuznetsova, M.A., Buterin, S.A. & Yurko, V.A. On Inverse Spectral Problems for Sturm–Liouville Differential Operators on Closed Sets. Lobachevskii J Math 42, 1201–1209 (2021). https://doi.org/10.1134/S1995080221060160

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  • DOI: https://doi.org/10.1134/S1995080221060160

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