On Hilbert's construction of positive polynomials

Details On Hilbert's construction of positive polynomials On Hilbert's construction of positive polynomials

2007-07-14

arxiv.org/abs/0707.2156v1

Mathematics

Algebraic Geometry

Scientific paper

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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