On spectral and pseudospectral functions of first-order symmetric systems

2014/07/21 by Vadim Mogilevskii, Mogilevskii, Vadim
Engineering · Mathematics · #34B08 #34B40 #34L10 #47A06 #47B25 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Material Science and Thermodynamics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1407.5398

openalex publication_date 2014/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider general (not necessarily Hamiltonian) 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∈\bR, is called a spectral (pseudospectral) function of such a system if the corresponding Fourier transform is an isometry (resp. partial isometry) from \LI into L²(\Si). The main result is a parametrization of all spectral and pseudospectral functions of a given system by means of a Nevanlinna boundary parameter τ. Similar parameterizations for various classes of boundary problems have earlier been obtained by Kac and Krein, Fulton, Langer and Textorius, Sakhnovich and others.

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