Inverse problems for matrix Sturm-Liouville operators

Abstract

Inverse spectral problems for nonselfadjoint matrix Sturm-Liouville differential operators on a finite interval and on the half-line are studied. As a main spectral characteristic, we introduce the so-called Weyl matrix and prove that the specification of the Weyl matrix uniquely determines the matrix potential and the coefficients of the boundary conditions. Moreover, for a finite interval, we also study the inverse problems of recovering matrix Sturm-Liouville operators from discrete spectral data (eigenvalues and “weight” numbers) and from a system of spectra. The results thus obtained are natural generalizations of the classical results in inverse problem theory for scalar Sturm-Liouville operators.