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 M.

N1 - Funding Information:
The second author is supported by COFIN grant 2004015437 and by INdAM; the third and the fourth authors are partially supported by NSF grant DMS-0456625; the third author is also partially supported by the Faculty Research Assignment from the College of William and Mary.

PY - 2007/5

Y1 - 2007/5

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

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U2 - 10.1007/s00020-007-1491-3

DO - 10.1007/s00020-007-1491-3

M3 - Article

AN - SCOPUS:34247641820

SN - 0378-620X

VL - 58

SP - 65

EP - 86

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

ER -