Abstract
In this paper, we propose an approach to inverse spectral problems for the n-th order (n≥2) ordinary differential operators with distribution coefficients. The inverse problems which consist in the reconstruction of the differential expression coefficients by the Weyl matrix and by several spectra are studied. We prove the uniqueness of solution for these inverse problems, by developing the method of spectral mappings. The results of this paper generalize the previously known results for the second-order differential operators with singular potentials and for the higher-order differential operators with regular coefficients. In the future, the approach of this paper can be used for constructive solution and for investigation of solvability of the considered inverse problems.
Highlights
In this paper, we study inverse spectral problems for the n-th order ordinary differential operators with distribution coefficients for n ≥ 2
In this paper, we propose an approach to inverse spectral problems for the n-th order (n ≥ 2) ordinary differential operators with distribution coefficients
The inverse problems which consist in the reconstruction of the differential expression coefficients by the Weyl matrix and by several spectra are studied
Summary
We study inverse spectral problems for the n-th order ordinary differential operators with distribution coefficients for n ≥ 2. By using the method of spectral mappings, Yurko [37,38] has constructed the inverse problem theory for the higher-order operators (3) with regular coefficients on the half-line and on a finite interval and, later on, for many other classes of differential operators and pencils. Beals and his followers [39] developed another approach to the higher-order inverse scattering problems on the line. The results of this paper with the previously known results for the second-order operators with singular potentials
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