Reconstruction of Higher-Order Differential Operators by Their Spectral Data

Natalia P. Bondarenko ()
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Natalia P. Bondarenko: Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, Samara 443086, Russia

Mathematics, 2022, vol. 10, issue 20, 1-32

Abstract: This paper is concerned with inverse spectral problems for higher-order ( n > 2 ) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either regular or distribution coefficients. Our approach is based on the reduction of an inverse problem to a linear equation in the Banach space of bounded infinite sequences. This equation is derived in a general form that can be applied to various classes of differential operators. The unique solvability of the linear main equation is also proved. By using the solution of the main equation, we derive reconstruction formulas for the differential expression coefficients in the form of series and prove the convergence of these series for several classes of operators. The results of this paper can be used for the constructive solution of inverse spectral problems and for the investigation of their solvability and stability.

Keywords: inverse spectral problems; higher-order differential operators; distribution coefficients; constructive solution; method of spectral mappings (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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