Polynomials that are positive on an interval

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Sums of Squares, Moment Matrices and Optimization Over Polynomials (2009, methodology): “Reznick [118] shows the following properties for Newton polytopes.”
Truncated K-moment problems in several variables (2005, background): “alized Schmu¨dgen-type theorem is valid. Indeed, recent advances in real algebra make it possible to concretely describe the polynomials nonnegative on certain noncompact semi-algebraic sets ([KuMa], [PoRe1], [PoRe2], [PoSc], [Pre], [Put2], [Sche]), so as to establish moment theorems via the previou”
Nonparametric Instrumental Variable Estimation Under Monotonicity (2015, methodology): “…over whole R but only over a compact sub-interval of R, one can use the same reasoning as above together with a result attributed to M. Fekete (see Powers and Reznick (2000), for example): for any polynomial f(x) with f(x) ≥ 0 for x ∈ [−1, 1], there are polynomials f1(x) and f2(x), non-negative…”