Spectral and pseudospectral functions of Hamiltonian systems: development of the results by Arov-Dym and Sakhnovich (Q2822222)

The author studies a Hamiltonian system NEWLINE\[NEWLINEJy'-B(t)y=\lambda \Delta (t)yNEWLINE\]NEWLINE defined on an interval \([a,b)\) with the regular endpoint \(a\). A pseudospectral function of a singular system is defined as a matrix-valued distribution function such that the generalized Fourier transform is a partial isometry with minimally possible kernel. All the spectral and pseudospectral functions are parametrized by a Nevanlinna boundary parameter. The results extend earlier ones by \textit{D. Z. Arov} and \textit{H. Dym} [Bitangential direct and inverse problems for systems of integral and differential equations, Cambridge University Press (2012; Zbl 1264.34004)] and by \textit{A. L. Sakhnovich} [Mat. Sb. 181, No. 11, 1510--1524 (1990; Zbl 0718.34112)].