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.References
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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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 801-813
- MSC (1991): Primary 46J10; Secondary 43A20
- DOI: https://doi.org/10.1090/S0002-9939-02-06574-7
- MathSciNet review: 1937418