Positive Polynomials on Closed Boxes - Diniz, Marcio A.; Stern, R. B.; Salazar, Luis E. (Trends in Computational and Applied Mathematics, 2019)
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 $\mathbb{R}^n$, $n>2$.