An inverse problem for the non-self-adjoint matrix Sturm-Liouville operator

TL;DR

This paper investigates the inverse spectral problem for non-self-adjoint matrix Sturm-Liouville operators on finite intervals, providing conditions for solvability and a constructive spectral mapping method.

Contribution

It introduces a new constructive approach for solving the inverse spectral problem for non-self-adjoint matrix Sturm-Liouville operators and characterizes spectral data.

Findings

Necessary and sufficient conditions for inverse problem solvability

Spectral data characterization for non-self-adjoint case

Extension of self-adjoint spectral characterization

Abstract

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary and sufficient conditions for the solvability of the inverse problem. Our approach is based on the constructive solution of the inverse problem by the method of spectral mappings. The characterization of the spectral data in the self-adjoint case is derived as a corollary of the main result.