### 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 2007 |

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

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## Cite this

*Integral Equations and Operator Theory*,

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