Isospectral sets and inverse problems for vector-valued Sturm–Liouville equations

Abstract

In this paper, we investigate inverse spectral problems for vectorial Sturm–Liouville equations via the matrix-valued Gelfand–Levitan equation. With this approach, we prove some uniqueness theorems for the even problem, mixed data problem and interior spectral data problem for vectorial Sturm–Liouville equations.