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Uniform Stability of Recovering Sturm–Liouville-Type Operators with Frozen Argument

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Abstract

In the last years, there has been considerable interest in inverse spectral problems for functional-differential operators with frozen argument. Until now, however, no aspects of their stability have been studied. One of the difficulties here is caused by the non-standard characterization of the spectra of such operators. In the present paper, we eliminate this gap and introduce a natural metric that allows us to obtain the Lipschitz stability on each ball of finite radius. Along with the previous results, this brings a final missing piece to the well-posedness of the inverse problem under consideration.

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Acknowledgements

The author thanks Sergey Buterin for the valuable comments that helped to improve the manuscript.

Funding

This research was supported by a grant of the Russian Science Foundation No. 22-21-00509, https://rscf.ru/project/22-21-00509/.

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  1. Department of Mathematics, Saratov State University, Astrakhanskaya 83, Saratov, Russia, 410012

    Maria Kuznetsova

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  1. Maria Kuznetsova
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Correspondence to Maria Kuznetsova.

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Kuznetsova, M. Uniform Stability of Recovering Sturm–Liouville-Type Operators with Frozen Argument. Results Math 78, 169 (2023). https://doi.org/10.1007/s00025-023-01945-z

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