Extremal properties of outer polynomial factors

Author:
Scott McCullough

Journal:
Proc. Amer. Math. Soc. **132** (2004), 815-825

MSC (2000):
Primary 47A68; Secondary 47A57

DOI:
https://doi.org/10.1090/S0002-9939-03-07122-3

Published electronically:
July 28, 2003

MathSciNet review:
2019960

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a positive polynomial of degree , then its outer factor 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 . 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:
https://doi.org/10.1090/S0002-9939-03-07122-3

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