Article
Ufa Mathematical Journal
Volume 7, Number 2, pp. 115-136
On spectral and pseudospectral functions of first-order symmetric systems
Mogilevskii V.I.
DOI:10.13108/2015-7-2-115
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We consider first-order symmetric system $J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b) $ with the regular endpoint $a$. A distribution matrix-valued function $\Si(s), \; s\in\bR,$ is called a pseudospectral function of such a system if the corresponding Fourier transform is a partial isometry with the minimally possible kernel. The main result is a parametrization of all pseudospectral functions of a given system by means of a Nevanlinna boundary parameter $\tau$. Similar parameterizations for regular systems have earlier been obtained by Arov and Dym, Langer and Textorius, A. Sakhnovich.