## 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.## References

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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. - © 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

Dedicated: In memory of Marvin Rosenblum