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

D. Alpay; A. Dijksma; H. Langer

doi:10.1016/j.laa.2004.02.037

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

D. Alpay
, A. Dijksma
, H. Langer

Department of Mathematics

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

9 Scopus citations

Abstract

We prove that a 2×2 matrix polynomial which is J-unitary on the real line can be written as a product of normalized elementary J-unitary factors and a J-unitary constant. In the second part we give an algorithm for this factorization using an analog of the Schur transformation.

Original language	English
Pages (from-to)	313-342
Number of pages	30
Journal	Linear Algebra and Its Applications
Volume	387
Issue number	1-3 SUPPL.
DOIs	https://doi.org/10.1016/j.laa.2004.02.037
State	Published - 1 Aug 2004

Keywords

Elementary factor
Generalized Nevanlinna function
Indefinite metric
J-unitary matrix polynomial
Minimal factorization
Moment problem
Reproducing kernel Pontryagin space
Schur transform

ASJC Scopus subject areas

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

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10.1016/j.laa.2004.02.037

Cite this

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title = "Factorization of J-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions",

abstract = "We prove that a 2×2 matrix polynomial which is J-unitary on the real line can be written as a product of normalized elementary J-unitary factors and a J-unitary constant. In the second part we give an algorithm for this factorization using an analog of the Schur transformation.",

keywords = "Elementary factor, Generalized Nevanlinna function, Indefinite metric, J-unitary matrix polynomial, Minimal factorization, Moment problem, Reproducing kernel Pontryagin space, Schur transform",

author = "D. Alpay and A. Dijksma and H. Langer",

year = "2004",

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doi = "10.1016/j.laa.2004.02.037",

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T1 - Factorization of J-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions

AU - Alpay, D.

AU - Dijksma, A.

AU - Langer, H.

PY - 2004/8/1

Y1 - 2004/8/1

N2 - We prove that a 2×2 matrix polynomial which is J-unitary on the real line can be written as a product of normalized elementary J-unitary factors and a J-unitary constant. In the second part we give an algorithm for this factorization using an analog of the Schur transformation.

AB - We prove that a 2×2 matrix polynomial which is J-unitary on the real line can be written as a product of normalized elementary J-unitary factors and a J-unitary constant. In the second part we give an algorithm for this factorization using an analog of the Schur transformation.

KW - Elementary factor

KW - Generalized Nevanlinna function

KW - Indefinite metric

KW - J-unitary matrix polynomial

KW - Minimal factorization

KW - Moment problem

KW - Reproducing kernel Pontryagin space

KW - Schur transform

UR - https://www.scopus.com/pages/publications/2942527678

U2 - 10.1016/j.laa.2004.02.037

DO - 10.1016/j.laa.2004.02.037

M3 - Article

AN - SCOPUS:2942527678

SN - 0024-3795

VL - 387

SP - 313

EP - 342

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3 SUPPL.

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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