Preserving positive polynomials and beyond
Julius Borcea, Alexander Emilevich Guterman, Boris Zalmanovich Shapiro · arXiv (Cornell University) · 2008
Following the classical approach of Pólya-Schur theory we initiate in this paper the study of linear operators acting on $\mathbb{R}[x]$ and preserving either the set of positive univariate polynomials or similar sets of non-negative and elliptic polynomials.