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

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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",

note = "Funding Information: Keywords: Schur transform; Generalized Nevanlinna function; Moment problem; Reproducing kernel Pontryagin space; Indefinite metric; J -unitary matrix polynomial; Elementary factor; Minimal factorization The research for this paper was supported by the Research Training Network HPRN-CT-2000-00116 of the European Union. ∗ Corresponding author. Tel.: +972-8-646-1603; fax: +972-8-647-7648. E-mail addresses: dany@math.bgu.ac.il (D. Alpay), dijksma@math.rug.nl (A. Dijksma), hlanger@mail.zserv.tuwien.ac.at (H. Langer).",

year = "2004",

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

language = "English",

volume = "387",

pages = "313--342",

journal = "Linear Algebra and Its Applications",

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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.

N1 - Funding Information: Keywords: Schur transform; Generalized Nevanlinna function; Moment problem; Reproducing kernel Pontryagin space; Indefinite metric; J -unitary matrix polynomial; Elementary factor; Minimal factorization The research for this paper was supported by the Research Training Network HPRN-CT-2000-00116 of the European Union. ∗ Corresponding author. Tel.: +972-8-646-1603; fax: +972-8-647-7648. E-mail addresses: dany@math.bgu.ac.il (D. Alpay), dijksma@math.rug.nl (A. Dijksma), hlanger@mail.zserv.tuwien.ac.at (H. Langer).

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 - http://www.scopus.com/inward/record.url?scp=2942527678&partnerID=8YFLogxK

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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