Hyperbolicity preservers and majorization

Abstract

The majorization order on $\RR^n$ induces a natural partial ordering on the space of univariate hyperbolic polynomials of degree $n$. We characterize all linear operators on polynomials that preserve majorization, and show that it is sufficient (modulo obvious degree constraints) to preserve hyperbolicity.

4 pages, Published as C. R. Math. Acad. Sci. Paris 348 (2010), 843-846

References in corpus (3)

• Polynomials with the half-plane property and matroid theory
• The Lax conjecture is true
• Polya-Schur master theorems for circular domains and their boundaries

Cited by in corpus (2)

• On the Further Structure of the Finite Free Convolutions
• Positively Hyperbolic Varieties, Tropicalization, and Positroids