English

Positive Polynomials on closed boxes

Classical Analysis and ODEs 2020-06-16 v2

Abstract

We present two different proofs that positive polynomials on closed boxes of R2\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 Rn\mathbb{R}^n, n>2n>2.

Keywords

Cite

@article{arxiv.1610.01437,
  title  = {Positive Polynomials on closed boxes},
  author = {Marcio Alves Diniz and Luis Ernesto Salasar and Rafael Bassi Stern},
  journal= {arXiv preprint arXiv:1610.01437},
  year   = {2020}
}
R2 v1 2026-06-22T16:11:31.562Z