Spectral Analysis for the Matrix Sturm-Liouville Operator on a Finite Interval

TL;DR

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

Contribution

It introduces a new constructive procedure for solving the inverse spectral problem for matrix Sturm-Liouville operators on finite intervals.

Findings

Spectral characteristics are characterized in detail.

A constructive method for the inverse problem is developed.

Necessary and sufficient conditions for solvability are established.

Abstract

The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with necessary and sufficient conditions for its solvability is obtained.