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Canonical factorization of continuous functions on the $d$-torus

Authors: Torsten Ehrhardt and Cornelis V. M. van der Mee
Journal: Proc. Amer. Math. Soc. 131 (2003), 801-813
MSC (1991): Primary 46J10; Secondary 43A20
Published electronically: July 26, 2002
MathSciNet review: 1937418
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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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Additional Information

Torsten Ehrhardt
Affiliation: Fakultät für Mathematik, Technische Universität Chemnitz, 09107 Chemnitz, Germany

Cornelis V. M. van der Mee
Affiliation: Dipartimento di Matematica, Università di Cagliari, via Ospedale 72, 09124 Cagliari, Italy

Keywords: Canonical factorization, Wiener algebra, maximal ideal space
Received by editor(s): July 18, 2001
Received by editor(s) in revised form: October 12, 2001
Published electronically: July 26, 2002
Additional Notes: This research was partially supported by INdAM-GNCS and MURST
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society