On several aspects of \(J\)-inner functions in Schur analysis
type: Item
instance of: scholarly article
title: On several aspects of \(J\)-inner functions in Schur analysis
zbMATH Open document ID: 0917.30022
author: Karsten Müller
author: Adhemar Bultheel
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1999-04-06T00:00:00Z
review text: The paper is a survey devoted to present different subjets of Schur analysis. The authors play a particular attention to their so called \(J\)-inner functions and they concentrate on the Soviet roots of the theory. We can find several sections: Classical interpolation problems, Blaschke products and the Nevanlinna-Pick algorithm; Darlington synthesis and scattering theory; Operator theoretic interpolation problems and dilation theory; Potapov factorization of \(J\)-contractive functions; Non-negative definite kernels, fundamental matrix inequality, fundamental indentities and the generalized Nehari problem; Arov's investigations on Darlington realization generated by \(J\)-inner functions; On \(J\)-inner functions and generalized bitangential Schur-Nevanlinna-Pinck interpolation. The paper contains 166 references.
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 30-02
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 94C05
zbMATH DE Number: 1266793
zbMATH Keywords: moment problems
zbMATH Keywords: interpolation on the complex plane
zbMATH Keywords: Schur functions
zbMATH Keywords: dilatation theory
zbMATH Keywords: Darlington realization
zbMATH Keywords: scattering theory
reviewed by: Jorge Bustamante
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1266793