Factorization of \(J\)-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions

DOI10.1016/j.laa.2004.02.037zbMath1073.47507OpenAlexW2170541883MaRDI QIDQ1434401

Daniel Alpay, Heinz K. Langer, Aalt Dijksma

Publication date: 4 August 2004

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2004.02.037

zbMATH Keywords

reproducing kernel Pontryagin spacegeneralized Nevanlinna functionSchur transformJ-unitary matrix polynomial

Mathematics Subject Classification ID

Linear operator methods in interpolation, moment and extension problems (47A57) Linear operators on spaces with an indefinite metric (47B50) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (7)

\(J_{\ell}\)-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting ⋮ An operator approach to the indefinite Stieltjes moment problem ⋮ On the convergence of Padé approximations for generalized Nevanlinna functions ⋮ Truncated moment problems in the class of generalized Nevanlinna functions ⋮ Inverse problems for periodic generalized Jacobi matrices ⋮ Regularization of the indefinite Stieltjes moment problem ⋮ Entries of indefinite Nevanlinna matrices

Cites Work

• Fonctions méromorphes dans le cercle-unité et leurs séries de Taylor
• On hermitian block Hankel matrices, matrix polynomials, the Hamburger moment problem, interpolation and maximum entropy
• Minimal factorization of matrix and operator functions
• Topics in interpolation theory of rational matrix-valued functions
• The Schur algorithm for generalized Schur functions. II: Jordan chains and transformations of characteristic functions
• The Schur algorithm for generalized Schur functions. III: \(J\)-unitary matrix polynomials on the circle.
• On generalized resolvents of Hermitian relations in Krein spaces
• Some Hilbert Spaces of Entire Functions. II
• Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im RaumeIIx zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen
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