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

The matrix-valued Weyl–Titchmarsh functions M(λ) 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(λ)) and the residues of M(λ) 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. © 2009 Elsevier Inc. All rights reserved.