Weyl-Titchmarsh functions of vector-valued Sturm-Liouville operators on the unit interval

Abstract

The matrix-valued Weyl-Titchmarsh functions M(¸) of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collection of the eigenvalues (i.e., poles of M(¸)) and the residues of M(¸) is called the spectral data of the operator. The complete characterization of spectral data (or, equivalently, N £ N Weyl-Titchmarsh functions) corresponding to N £ N self-adjoint square-integrable matrix-valued potentials is given, if all N eigenvalues of the averaged potential are distinct.