Positive Polynomials on Closed Boxes

ABSTRACT

We present two different proofs that positive polynomials on closed boxes of ${ℝ}^2$ 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 ${ℝ}^n$, $n>2$.

Key words
polinômios positivos; hipercubo unitário; polinômios de Bernstein