Positive polynomials on closed boxes

Abstract

We present two different proofs that positive polynomials on closed boxes of the plane 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 higher-dimensional spaces.

Publication
In Tendências em Matemática Aplicada e Computacional
Rafael B. Stern
Rafael B. Stern
Professor of Statistics

I am an Assistant Professor at the Federal University of São Carlos. I have a B.A. in Statistics from University of São Paulo, a B.A. in Law from Pontifícia Universidade Católica in São Paulo, and a Ph.D. in Statistics from Carnegie Mellon University. I am currently a member of the Scientific Council of the Brazilian Association of Jurimetrics, an associate investigator at NeuroMat and a member of the Order of Attorneys of Brazil.