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Polynomials non-negative on a strip

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

Abstract: We prove that if is a polynomial with real coefficients which is non-negative on the strip $[0,1]\times \mathbb{R}$ , then 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

and

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
Email: marshall@math.usask.ca

DOI: 10.1090/S0002-9939-09-10016-3
PII: S 0002-9939(09)10016-3
Keywords: Positive polynomials, sums of squares, moment problem.
Received by editor(s): June 9, 2008, and in revised form, April 26, 2009
Posted: December 22, 2009
Additional Notes: This research was funded in part by an NSERC Discovery Grant.
Communicated by: Ted Chinburg
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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