Positive Polynomials on Closed Boxes
DOI:
https://doi.org/10.5540/tema.2019.020.03.509Keywords:
positive polynomials, unit box, Bernstein polynomialsAbstract
We present two different proofs that positive polynomials on closed boxes of $\mathbb{R}^2$ can be written as bivariate Bernstein polynomials with strictly positive coefficients.
Both strategies can be extended to prove the analogous result for polynomials that are positive on closed boxes of $\mathbb{R}^n$, $n>2$.
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