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Uniform stability of the inverse spectral problem for a convolution integro-differential operator

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  • Buterin, Sergey

Abstract

The operator of double differentiation perturbed by the composition of the differentiation operator and a convolution one on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the convolution kernel from the spectrum both in a weighted L2-norm and in a weighted uniform norm. For this purpose, we successively prove uniform stability of each step of the algorithm for solving this inverse problem in both norms. The obtained results reveal some essential difference from the classical inverse Sturm–Liouville problem.

Suggested Citation

  • Buterin, Sergey, 2021. "Uniform stability of the inverse spectral problem for a convolution integro-differential operator," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305476
    DOI: 10.1016/j.amc.2020.125592
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    References listed on IDEAS

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    1. Vladimir A. Zolotarev, 2019. "Inverse spectral problem for the operators with non‐local potential," Mathematische Nachrichten, Wiley Blackwell, vol. 292(3), pages 661-681, March.
    2. Hu, Yi-teng & Bondarenko, Natalia Pavlovna & Shieh, Chung-Tsun & Yang, Chuan-fu, 2019. "Traces and inverse nodal problems for Dirac-type integro-differential operators on a graph," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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