On the Construction of Isospectral Vectorial Sturm-Liouville Differential Equations

TL;DR

This paper extends the concept of constructing isospectral problems from scalar to vectorial Sturm-Liouville differential equations, revealing new relations and broadening the scope of spectral theory.

Contribution

It introduces a method for constructing isospectral vectorial Sturm-Liouville problems, generalizing previous scalar approaches and uncovering new mathematical relations.

Findings

Established relations between isospectral vectorial problems

Extended scalar methods to vectorial cases

Provided new insights into spectral properties

Abstract

The author extends the idea of Jodeit and Levitan for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are found.