Linear Operators $T:\mathbb{R}[x_1,\dots ,x_n]\to \mathbb{R}[x_1,\dots ,x_n]$ and $K$-Positivity Preserver: A Short Review

Abstract

In the current short review we present the latest developments on linear maps $T:\mathbb{R}[x_1,\dots ,x_n]\to \mathbb{R}[x_1,\dots ,x_n]$, especially of $K$-positivity preserver, i.e., $Tp\ge 0$ on $K\subseteq {\mathbb{R}}^n$ for all $p\in \mathbb{R}[x_1,\dots ,x_n]$ with $p\ge 0$ on $K$.