Inverse spectral problem for a third-order differential operator

2023/08/22 by Vladimir A. Zolotarev, Zolotarev, Vladimir A.
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2308.11575

openalex publication_date 2023/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system of integral linear equations is obtained. Via solution to this system, the potential is calculated. It is shown that the main parameters of the obtained system of equations are expressed via spectral data of the initial operator. It is established that the potential is unambiguously defined by the four spectra.

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