Hyperbolicity preservers and majorization

Details Hyperbolicity preservers and majorization Hyperbolicity preservers and majorization

2010-05-28

arxiv.org/abs/1005.5293v3

C. R. Math. Acad. Sci. Paris 348 (2010), no. 15-16, 843-846

Mathematics

Classical Analysis and ODEs

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

Scientific paper

10.1016/j.crma.2010.07.006

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.

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