Hyperbolicity preservers and majorization
Classical Analysis and ODEs
2012-04-18 v3 Complex Variables
Abstract
The majorization order on induces a natural partial ordering on the space of univariate hyperbolic polynomials of degree . We characterize all linear operators on polynomials that preserve majorization, and show that it is sufficient (modulo obvious degree constraints) to preserve hyperbolicity.
Cite
@article{arxiv.1005.5293,
title = {Hyperbolicity preservers and majorization},
author = {Julius Borcea and Petter Brändén},
journal= {arXiv preprint arXiv:1005.5293},
year = {2012}
}
Comments
4 pages, Published as C. R. Math. Acad. Sci. Paris 348 (2010), 843-846