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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Extremal properties of outer polynomial factors


Author: Scott McCullough
Journal: Proc. Amer. Math. Soc. 132 (2004), 815-825
MSC (2000): Primary 47A68; Secondary 47A57
Published electronically: July 28, 2003
MathSciNet review: 2019960
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Abstract: If $p(s)$ is a positive polynomial of degree $2d$, then its outer factor $q(s)$has the property that the magnitude of each of its coefficients is larger than the magnitude of the corresponding coefficient of any other factor. In fact, this extremal property holds over vector-valued factorizations $r(s)^{*}r(s)=p(s)$. Corollaries include a result for symmetric functions and complex conjugate pairs.


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Additional Information

Scott McCullough
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611-8105
Email: sam@math.ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07122-3
PII: S 0002-9939(03)07122-3
Keywords: Spectral factorization, outer factor, Hankel matrix, symmetric functions
Received by editor(s): February 26, 2002
Received by editor(s) in revised form: November 1, 2002
Published electronically: July 28, 2003
Additional Notes: This research was supported by NSF grant DMS-9970347
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society