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arXiv · 1610.01437

Positive Polynomials on closed boxes

Marcio Alves Diniz·Luis Ernesto Salasar·Rafael Bassi Stern
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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 $\mathbb{R}^n$, $n>2$.

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Marcio Alves Diniz, Luis Ernesto Salasar, Rafael Bassi Stern. 2016-09-26. Positive Polynomials on closed boxes. https://doi.org/10.5540/tema.2019.020.03.0509

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