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Direct and Inverse Problems of Spectral Analysis for Arbitrary-Order Differential Operators with Nonintegrable Regular Singularities

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Abstract

A short review is presented of results on the spectral theory of arbitrary-order ordinary differential operators with nonintegrable regular singularities. We establish properties of spectral characteristics, prove theorems on completeness of root functions in the corresponding spaces, prove expansion and equiconvergence theorems, and provide a solution of the inverse spectral problem for this class of operators.

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Authors and Affiliations

  1. Chernyshevskii Saratov National Research State University, Saratov, Russia

    V. A. Yurko

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  1. V. A. Yurko
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Correspondence to V. A. Yurko.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 2, Dedicated to the memory of Professor N. D. Kopachevsky, 2021.

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Yurko, V.A. Direct and Inverse Problems of Spectral Analysis for Arbitrary-Order Differential Operators with Nonintegrable Regular Singularities. J Math Sci 278, 194–205 (2024). https://doi.org/10.1007/s10958-024-06913-8

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  • DOI: https://doi.org/10.1007/s10958-024-06913-8

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