Positive Polynomials on Closed Boxes

Abstract

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 $\mathbb{R}^n$, $n>2$.

Keywords

• positive polynomials
• unit box
• Bernstein polynomials