Canonical factorization of continuous functions on the 𝑑-torus

Ehrhardt, Torsten; van der Mee, Cornelis

doi:10.1090/S0002-9939-02-06574-7

Canonical factorization of continuous functions on the $d$-torus
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by Torsten Ehrhardt and Cornelis V. M. van der Mee PDF

Proc. Amer. Math. Soc. 131 (2003), 801-813 Request permission

Abstract:

In this article we study the canonical factorization of continuous complex-valued functions on the $d$-dimensional torus belonging to a weighted Wiener algebra with respect to a linear order on the $d$-tuples of integers. It is proved that a function has a canonical factorization in this algebra if and only if it has a logarithm belonging to this algebra. A second characterization is given in terms of winding numbers. Moreover, the maximal ideal spaces of the relevant Banach algebras are identified.

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