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On an Inverse Spectral Problem for the Convolution Integro-Differential Operator of Fractional Order

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Abstract

An inverse spectral problem for the convolution integro-differential operator of fractional order \(\alpha >2\) is studied. We show that specification of one spectrum determines such operator uniquely independently of particular value of \(\alpha \). The convolution kernel can be recovered by solving a certain nonlinear equation.

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Acknowledgements

This work was supported by the Russian Science Foundation (Project No. 17-11-01193).

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

    Mikhail Ignatyev

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  1. Mikhail Ignatyev
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Correspondence to Mikhail Ignatyev.

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Ignatyev, M. On an Inverse Spectral Problem for the Convolution Integro-Differential Operator of Fractional Order. Results Math 73, 34 (2018). https://doi.org/10.1007/s00025-018-0800-2

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  • DOI: https://doi.org/10.1007/s00025-018-0800-2

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