Spectral and pseudospectral functions of Hamiltonian systems: development of the results by Arov-Dym and Sakhnovich - Mogilevskii, V. I. (Methods of Functional Analysis and Topology, 2015)
The main object of the paper is a Hamiltonian system J y’-B(t)y=λΔ(t) y defined on an interval [a,b) with the regular endpoint a. We define a pseudospectral function of a singular system as a matrix-valued distribution function such that the generalized Fourier transform is a partial isometry with the minimally possible kernel. Moreover, we parameterize all spectral and pseudospectral functions of a given system by means of a Nevanlinna boundary parameter. The obtained results develop the results by Arov-Dym and Sakhnovich in this direction.