Augmented Schur Parameters for Generalized Nevanlinna Functions and Approximation

DOI10.1007/978-3-7643-8911-6_1zbMath1161.41004OpenAlexW120012345MaRDI QIDQ3613517

Daniel Alpay, Heinz K. Langer, Aalt Dijksma

Publication date: 12 March 2009

Published in: Spectral Theory in Inner Product Spaces and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-7643-8911-6_1

zbMATH Keywords

approximationSchur algorithmgeneralized Nevanlinna functionSchur transform(-i\(J\))-unitary matrix function

Mathematics Subject Classification ID

Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80) Approximation by rational functions (41A20) Linear operator methods in interpolation, moment and extension problems (47A57) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Meromorphic functions of one complex variable (general theory) (30D30) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (1)

Schur Analysis in an Indefinite Setting

Cites Work

• \(J_{\ell}\)-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting
• Structured invariant spaces of vector valued rational functions, Hermitian matrices, and a generalization of the Iohvidov laws
• The Schur transformation for generalized Nevanlinna functions: interpolation and self-adjoint operator realizations
• Minimal factorization of matrix and operator functions
• The Schur algorithm for generalized Schur functions. III: \(J\)-unitary matrix polynomials on the circle.
• The transformation of Issai Schur and related topics in an indefinite setting
• Contributions of Issai Schur to Analysis
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