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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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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