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Polynomials non-negative on a strip

Author: M. Marshall
Journal: Proc. Amer. Math. Soc. 138 (2010), 1559-1567
MSC (2010): Primary 14P99; Secondary 12D15, 12E05
Published electronically: December 22, 2009
MathSciNet review: 2587439
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if $ f(x,y)$ is a polynomial with real coefficients which is non-negative on the strip $ [0,1]\times \mathbb{R}$, then $ f(x,y)$ has a presentation of the form

$\displaystyle f(x,y) = \sum_{i=1}^k g_i(x,y)^2+\sum_{j=1}^{\ell}h_j(x,y)^2x(1-x),$

where the $ g_i(x,y)$ and $ h_j(x,y)$ are polynomials with real coefficients.

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Additional Information

M. Marshall
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, Canada, S7N 5E6

Keywords: Positive polynomials, sums of squares, moment problem.
Received by editor(s): June 9, 2008
Received by editor(s) in revised form: April 26, 2009
Published electronically: December 22, 2009
Additional Notes: This research was funded in part by an NSERC Discovery Grant.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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