Regularization and Inverse Spectral Problems for Differential Operators with Distribution Coefficients

Natalia P. Bondarenko ()
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Natalia P. Bondarenko: Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia

Mathematics, 2023, vol. 11, issue 16, 1-23

Abstract: In this paper, we consider a class of matrix functions that contains regularization matrices of Mirzoev and Shkalikov for differential operators with distribution coefficients of order n ≥ 2 . We show that every matrix function of this class is associated with some differential expression. Moreover, we construct the family of associated matrices for a fixed differential expression. Furthermore, our regularization results are applied to inverse spectral theory. We study a new type of inverse spectral problems, which consist of the recovery of distribution coefficients from the spectral data independently of the associated matrix. The uniqueness theorems are proved for the inverse problems by the Weyl–Yurko matrix and by the discrete spectral data. As examples, we consider the cases n = 2 and n = 4 in more detail.

Keywords: higher-order differential operators; distribution coefficients; regularization; inverse spectral problems; Weyl–Yurko matrix; uniqueness theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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