Factorization in weighted wiener matrix algebras on linearly ordered abelian groups

Torsten Ehrhardt, Cornelis Van Der Mee, Leiba Rodman, Ilya Spitkovsky

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)65-86
Number of pages22
JournalIntegral Equations and Operator Theory
Volume58
Issue number1
DOIs
StatePublished - May 1 2007

Fingerprint

Wiener Algebra
Ordered Group
Matrix Algebra
Abelian group
Factorization
Matrix Function
Linearly
Winding number
Compact Group
Linear Order
Connected Components
Invertible
Equivalence
Scalar
Topology
Algebra

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

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

In: Integral Equations and Operator Theory, Vol. 58, No. 1, 01.05.2007, p. 65-86.

Research output: Contribution to journalArticle

Ehrhardt, Torsten ; Van Der Mee, Cornelis ; Rodman, Leiba ; Spitkovsky, Ilya. / Factorization in weighted wiener matrix algebras on linearly ordered abelian groups. In: Integral Equations and Operator Theory. 2007 ; Vol. 58, No. 1. pp. 65-86.
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