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arXiv · 0707.2156

On Hilbert's construction of positive polynomials

Bruce Reznick
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Abstract

In 1888, Hilbert described how to find real polynomials in more than one variable which take only non-negative values but are not a sum of squares of polynomials. His construction was so restrictive that no explicit examples appeared until the late 1960s. We revisit and generalize Hilbert's construction and present many such polynomials.

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Bruce Reznick. 2007-07-14. On Hilbert's construction of positive polynomials. https://arxiv.org/abs/0707.2156

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