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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Email: tehrhard@mathematik.tu-chemnitz.de

Cornelis V. M. van der Mee
Affiliation: Dipartimento di Matematica, Università di Cagliari, via Ospedale 72, 09124 Cagliari, Italy
Email: cornelis@bugs.unica.it

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06574-7
PII: S 0002-9939(02)06574-7
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