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arXiv · 1005.5293

Hyperbolicity preservers and majorization

Julius Borcea·Petter Brändén
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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.

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Julius Borcea, Petter Brändén. 2010-08-30. Hyperbolicity preservers and majorization. https://doi.org/10.1016/j.crma.2010.07.006

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