This article is cited in 5 papers

On spectral and pseudospectral functions of first-order symmetric systems

V. I. Mogilevskii

Department of Differential Equations, Bashkir State University, 32 Zaki Validi, Ufa, 450076, Russia

Abstract: 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, Fourier transform, characteristic matrix.

MSC: 34B08, 34B40, 34L10, 47A06, 47B25

Received: 20.10.2014

Language: English

 English version: Ufa Mathematical Journal, 2015, 7:2, 115–136

Bibliographic databases:

• 
• 
•