On spectral and pseudospectral functions of first-order symmetric systems

We consider general (not necessarily Hamiltonian) first-order symmetric system $J{y}^{\mathrm{\prime }}-B(t)y=\text{D}(t)f(t)$ on an interval $\text{cI}=[a,b)$ with the regular endpoint $a$. A distribution matrix-valued function $\text{Si}(s),s\in \text{bR},$ is called a spectral (pseudospectral) function of such a system if the corresponding Fourier transform is an isometry (resp. partial isometry) from $\text{LI}$ into $L^2(\text{Si})$. The main result is a parametrization of all spectral and pseudospectral functions of a given system by means of a Nevanlinna boundary parameter $\tau$. Similar parameterizations for various classes of boundary problems have earlier been obtained by Kac and Krein, Fulton, Langer and Textorius, Sakhnovich and others.