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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Outer factorizations in one and several variables
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by Michael A. Dritschel and Hugo J. Woerdeman PDF
Trans. Amer. Math. Soc. 357 (2005), 4661-4679 Request permission

Abstract:

A multivariate version of Rosenblum’s Fejér-Riesz theorem on outer factorization of trigonometric polynomials with operator coefficients is considered. Due to a simplification of the proof of the single variable case, new necessary and sufficient conditions for the multivariable outer factorization problem are formulated and proved.
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Additional Information
  • Michael A. Dritschel
  • Affiliation: School of Mathematics and Statistics, Merz Court, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, United Kingdom
  • Email: m.a.dritschel@newcastle.ac.uk
  • Hugo J. Woerdeman
  • Affiliation: Department of Mathematics, The College of William & Mary, Williamsburg, Virginia 23185-8795 – and – Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B3001 Heverlee, Belgium
  • Address at time of publication: Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104
  • MR Author ID: 183930
  • Email: hugo@math.drexel.edu
  • Received by editor(s): March 1, 2004
  • Published electronically: June 21, 2005
  • Additional Notes: The first author’s research was supported by the Engineering and Physical Sciences Research Council (EPSRC) and by the European Community’s Human Potential Programme Under Contract HPRN-CT-2000-00116 (Analysis And Operators).
    The second author’s research was supported in part by the National Science Foundation (NSF), as well as a Faculty Research Assignment (FRA) Grant from the College of William & Mary.

  • Dedicated: In memory of Marvin Rosenblum
  • © Copyright 2005 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 4661-4679
  • MSC (2000): Primary 47A68, 47B35, 15A48
  • DOI: https://doi.org/10.1090/S0002-9947-05-03814-6
  • MathSciNet review: 2156726