Polynomials non-negative on a strip

Marshall, M.

doi:10.1090/S0002-9939-09-10016-3

Polynomials non-negative on a strip
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Proc. Amer. Math. Soc. 138 (2010), 1559-1567 Request permission

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 \[ f(x,y) = \sum _{i=1}^k g_i(x,y)^2+\sum _{j=1}^{\ell }h_j(x,y)^2x(1-x),\] where the $g_i(x,y)$ and $h_j(x,y)$ are polynomials with real coefficients.

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