Characteristic matrices and spectral functions of first order symmetric systems with maximal deficiency index of the minimal relation - Mogilevskii, V. I. (Methods of Functional Analysis and Topology, 2015)
Let H be a finite dimensional Hilbert space and let [H] be the set of all li ear operators in H. We consider first-order symmetric system J y’-B(t)y=Λ(t) f(t) with [H]-valued coefficients defined on an interval [a,b) with the regular endpoint a. It is assumed that the corresponding minimal relation T_min has maximally possible deficiency index n_+(T_min)=H. The main result is a parametrization of all characteristic matrices and pseudospectral (spectral) functions of a given system by means of a Nevanlinna type boundary parameter τ. Similar parametrization for regular systems has earlier been obtained by Langer and Textorius. We also show that the coefficients of the parametrization form the matrix W(λ) with the properties similar to those of the resolvent matrix in the extension theory of symmetric operators.