Geodesic
On spectral and pseudospectral functions of first-order symmetric systems
Ufa mathematical journal, Tome 7 (2015) no. 2, pp. 115-136

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We consider first-order symmetric system $Jy'-B(t)y=\Delta(t)f(t)$ on an interval $\mathcal I=[a,b)$ with the regular endpoint $a$. A distribution matrix-valued function $\Sigma(s)$, $s\in\mathbb R$, 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.
Keywords: First-order symmetric system, spectral function, pseudospectral function, characteristic matrix.
Mots-clés : Fourier transform 
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V. I. Mogilevskii. On spectral and pseudospectral functions of first-order symmetric systems. Ufa mathematical journal, Tome 7 (2015) no. 2, pp. 115-136. http://geodesic.mathdoc.fr/item/UFA_2015_7_2_a8/