On the roots of polynomials with log-convex coefficients

Abstract: In the spirit of the work developed for the Steiner polynomial of convex bodies, we investigate geometric properties of the roots of a general family of n-th degree polynomials closely related to that of dual Steiner polynomials of star bodies, deriving, as a consequence, further properties for the roots of the latter. We study the structure of the set of roots of such polynomials, showing that it is a closed convex cone in the upper half-plane, which covers its interior when n tends to infinity, and giving its precise description for every natural n\geq 2. This is a joint work with J. Yepes-Nicolas and M. Tarraga.

analysis of PDEsmetric geometryprobability

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

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