Inverse problems for the matrix Sturm–Liouville equation on a finite interval

Abstract

Inverse spectral problems are studied for the non-self-adjoint matrix Sturm–Liouville differential equation on a finite interval. We give formulations of the inverse problems, prove the corresponding uniqueness theorems, and provide a constructive procedure for the solution of the inverse problems by the method of spectral mappings. The obtained results are a natural generalization of the classical results in inverse problem theory for scalar Sturm–Liouville operators.