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Transactions of the American Mathematical Society

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Outer factorizations in one and several variables

Authors: Michael A. Dritschel and Hugo J. Woerdeman
Journal: Trans. Amer. Math. Soc. 357 (2005), 4661-4679
MSC (2000): Primary 47A68, 47B35, 15A48
Published electronically: June 21, 2005
MathSciNet review: 2156726
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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

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

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
Article copyright: © Copyright 2005 American Mathematical Society