On Hilbert's construction of positive polynomials

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.

Cited by in corpus (2)

• Dimensional Differences between Nonnegative Polynomials and Sums of Squares
• Existence of positive definite noncoercive sums of squares