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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 2, Pages 123–144 (Mi ufa283)  

This article is cited in 2 scientific papers (total in 2 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.

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English version:
Ufa Mathematical Journal, 2015, 7:2, 115–136 (PDF, 651 kB); https://doi.org/10.13108/2015-7-2-115

Bibliographic databases:

MSC: 34B08, 34B40, 34L10, 47A06, 47B25
Received: 20.10.2014
Language:

Citation: V. I. Mogilevskii, “On spectral and pseudospectral functions of first-order symmetric systems”, Ufimsk. Mat. Zh., 7:2 (2015), 123–144; Ufa Math. J., 7:2 (2015), 115–136

Citation in format AMSBIB
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\pages 123--144
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. Mogilevskii, “Spectral functions for the vector-valued Fourier transform”, J. Funct. space, 2018, 9584150  crossref  mathscinet  zmath  isi  scopus
    2. V. I. Mogilevskii, “Symmetric extensions of symmetric linear relations (operators) preserving the multivalued part”, Methods Funct. Anal. Topol., 24:2 (2018), 152–177  mathscinet  zmath  isi
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