An inverse problem for the quadratic pencil of non-self-adjoint matrix operators on the half-line

TL;DR

This paper addresses the inverse problem of reconstructing a non-self-adjoint matrix Sturm-Liouville pencil on the half-line from its Weyl matrix, providing a uniqueness theorem and a constructive solution algorithm.

Contribution

It introduces a novel inverse problem framework for non-self-adjoint matrix pencils and offers a constructive method for their reconstruction from spectral data.

Findings

Proved a uniqueness theorem for the inverse problem.

Developed a constructive algorithm for reconstruction.

Enhanced understanding of spectral properties of non-self-adjoint operators.

Abstract

We consider a pencil of non-self-adjoint matrix Sturm-Liouville operators on the half line and study the inverse problem of constructing this pencil by its Weyl matrix. A uniqueness theorem is proved, and a constructive algorithm for the solution is obtained.