Jℓ-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting

D. Alpay; A. Dijksma; H. Langer

doi:10.1016/j.laa.2006.06.010

J_ℓ-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting

D. Alpay
, A. Dijksma
, H. Langer

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We introduce a Schur transformation for generalized Nevanlinna functions and show that it can be used in obtaining the unique minimal factorization of a class of rational J_ℓ-unitary 2 × 2 matrix functions into elementary factors from the same class.

Original language	English
Pages (from-to)	675-709
Number of pages	35
Journal	Linear Algebra and Its Applications
Volume	419
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2006.06.010
State	Published - 1 Dec 2006

Keywords

Elementary rational matrix functions
Generalized Nevanlinna functions
J-unitarity on the real line
Kernels with negative squares
Minimal factorizations
Reproducing kernel Pontryagin spaces
Schur transformation

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.laa.2006.06.010

Cite this

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title = "Jℓ-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting",

abstract = "We introduce a Schur transformation for generalized Nevanlinna functions and show that it can be used in obtaining the unique minimal factorization of a class of rational Jℓ-unitary 2 × 2 matrix functions into elementary factors from the same class.",

keywords = "Elementary rational matrix functions, Generalized Nevanlinna functions, J-unitarity on the real line, Kernels with negative squares, Minimal factorizations, Reproducing kernel Pontryagin spaces, Schur transformation",

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AU - Dijksma, A.

AU - Langer, H.

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AB - We introduce a Schur transformation for generalized Nevanlinna functions and show that it can be used in obtaining the unique minimal factorization of a class of rational Jℓ-unitary 2 × 2 matrix functions into elementary factors from the same class.

KW - Elementary rational matrix functions

KW - Generalized Nevanlinna functions

KW - J-unitarity on the real line

KW - Kernels with negative squares

KW - Minimal factorizations

KW - Reproducing kernel Pontryagin spaces

KW - Schur transformation

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