Hamiltonian systems, Titchmarsh-Weyl coefficients, and models

This note concerns an eigenvalue problem for a Hamiltonian system of ordinary differential equations in an L(2)-space with a boundary condition depending linearly on the eigenvalue parameter. We show that the spectral properties (in particular, the embedded eigenvalues) of this problem can be obtained from the Titchmarsh-Weyl coefficients. These coefficients appear in formulas for the generalized resolvent associated with a selfadjoint linearization of the problem in a Pontryagin space. They are generalized Nevanlinna functions and have representations in terms of selfadjoint relations (models) and integral representations. The note is based on the joint paper [1].