\(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. IV: Direct and inverse bitangential input scattering problems
type: Item
instance of: scholarly article
title: \(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. IV: Direct and inverse bitangential input scattering problems
zbMATH Open document ID: 1040.34012
DOI: 10.1007/BF01196514
author: Damir Z. Arov
author: Harry Dym
published in: Integral Equations and Operator Theory
publication date: 2002-01-01T00:00:00Z
review text: The paper is a continuation of the authors' investigations [Part I, Integral Equations Oper. Theory 29, No. 4, 373--454 (1997; Zbl 0902.30026]), II, ibid. 36, No. 1, 11--70 (2000; Zbl 0951.30029), III, ibid. 36, No. 2, 127--181 (2000; Zbl 0998.30037)] of inverse problems for canonical differential and integral systems of equations. In the paper under review the inverse input scattering problems are formulated and analyzed for canonical integral systems. Special attention is paid to the case when the input scattering matrix is of Wiener class. Formulas for the solution of the inverse input scattering problem are obtained by reproducing kernel Hilbert space methods. A number of illustrative examples are presented. For Part v, cf. ibid. 43, No.1, 68-129 (2002; Zbl 1009.34007).
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 30D99
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 47B32
zbMATH DE Number: 1754737
zbMATH Keywords: integral equation
zbMATH Keywords: holomorphic matrix-valued function
zbMATH Keywords: scattering problem
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01196514
OpenAlex ID: W2053650105
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description: scientific article; zbMATH DE number 1754737