\(J_{\ell}\)-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting

DOI10.1016/j.laa.2006.06.010zbMath1113.47009OpenAlexW2170779380MaRDI QIDQ865432

Aalt Dijksma, Daniel Alpay, Heinz K. Langer

Publication date: 14 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.06.010

zbMATH Keywords

Schur transformationminimal factorizationselementary rational matrix functionsgeneralised Nevanlinna functionsJ-unitaritykernel with negative squaresreproducing kernel Pontryagin spaces

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Linear operator methods in interpolation, moment and extension problems (47A57) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Moment problems and interpolation problems in the complex plane (30E05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Linear operators on spaces with an indefinite metric (47B50)

Related Items (3)

Schur Analysis in an Indefinite Setting ⋮ A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks ⋮ Augmented Schur Parameters for Generalized Nevanlinna Functions and Approximation

Cites Work

• Fonctions méromorphes dans le cercle-unité et leurs séries de Taylor
• Structured invariant spaces of vector valued rational functions, Hermitian matrices, and a generalization of the Iohvidov laws
• Topics in interpolation theory of rational matrix-valued functions
• Schur functions, operator colligations, and reproducing kernel Pontryagin spaces
• 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.
• Factorization of \(J\)-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions
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