An inverse spectral problem for the matrix Sturm-Liouville operator on the half-line

TL;DR

This paper addresses the inverse spectral problem for matrix Sturm-Liouville operators on the half-line, providing necessary and sufficient conditions for reconstructing the operator from the Weyl matrix, including the self-adjoint case.

Contribution

It establishes a complete characterization of spectral data for non-self-adjoint matrix Sturm-Liouville operators and extends results to the self-adjoint case.

Findings

Derived necessary and sufficient conditions for the Weyl matrix

Characterized spectral data for self-adjoint operators

Provided a reconstruction method for the operator

Abstract

The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix. The main result of the paper is the necessary and sufficient conditions on the Weyl matrix of the non-self-adjoint matrix Sturm-Liouville operator. We also investigate the self-adjoint case and obtain the characterization of the spectral data as a corollary of our general result.