### Abstract

Factorizations of Wiener-Hopf type of elements of weighted Wiener algebras of continuous matrix-valued functions on a compact abelian group are studied. The factorizations are with respect to a fixed linear order in the character group (considered with the discrete topology). Among other results, it is proved that if a matrix function has a canonical factorization in one such matrix Wiener algebra then it belongs to the connected component of the identity of the group of invertible elements in the algebra, and moreover, the factors of the canonical factorization depend continuously on the matrix function. In the scalar case, complete characterizations of canonical and noncanonical factorability are given in terms of abstract winding numbers. Wiener-Hopf equivalence of matrix functions with elements in weighted Wiener algebras is also discussed.

Original language | English (US) |
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Pages (from-to) | 65-86 |

Number of pages | 22 |

Journal | Integral Equations and Operator Theory |

Volume | 58 |

Issue number | 1 |

DOIs | |

State | Published - May 1 2007 |

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### Keywords

- Compact abelian group
- Wiener algebra
- Wiener-Hopf factorization

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis

### Cite this

*Integral Equations and Operator Theory*,

*58*(1), 65-86. https://doi.org/10.1007/s00020-007-1491-3

**Factorization in weighted wiener matrix algebras on linearly ordered abelian groups.** / Ehrhardt, Torsten; Van Der Mee, Cornelis; Rodman, Leiba; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Integral Equations and Operator Theory*, vol. 58, no. 1, pp. 65-86. https://doi.org/10.1007/s00020-007-1491-3

}

TY - JOUR

T1 - Factorization in weighted wiener matrix algebras on linearly ordered abelian groups

AU - Ehrhardt, Torsten

AU - Van Der Mee, Cornelis

AU - Rodman, Leiba

AU - Spitkovsky, Ilya

PY - 2007/5/1

Y1 - 2007/5/1

N2 - Factorizations of Wiener-Hopf type of elements of weighted Wiener algebras of continuous matrix-valued functions on a compact abelian group are studied. The factorizations are with respect to a fixed linear order in the character group (considered with the discrete topology). Among other results, it is proved that if a matrix function has a canonical factorization in one such matrix Wiener algebra then it belongs to the connected component of the identity of the group of invertible elements in the algebra, and moreover, the factors of the canonical factorization depend continuously on the matrix function. In the scalar case, complete characterizations of canonical and noncanonical factorability are given in terms of abstract winding numbers. Wiener-Hopf equivalence of matrix functions with elements in weighted Wiener algebras is also discussed.

AB - Factorizations of Wiener-Hopf type of elements of weighted Wiener algebras of continuous matrix-valued functions on a compact abelian group are studied. The factorizations are with respect to a fixed linear order in the character group (considered with the discrete topology). Among other results, it is proved that if a matrix function has a canonical factorization in one such matrix Wiener algebra then it belongs to the connected component of the identity of the group of invertible elements in the algebra, and moreover, the factors of the canonical factorization depend continuously on the matrix function. In the scalar case, complete characterizations of canonical and noncanonical factorability are given in terms of abstract winding numbers. Wiener-Hopf equivalence of matrix functions with elements in weighted Wiener algebras is also discussed.

KW - Compact abelian group

KW - Wiener algebra

KW - Wiener-Hopf factorization

UR - http://www.scopus.com/inward/record.url?scp=34247641820&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247641820&partnerID=8YFLogxK

U2 - 10.1007/s00020-007-1491-3

DO - 10.1007/s00020-007-1491-3

M3 - Article

VL - 58

SP - 65

EP - 86

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -