We investigate the roots of a family of geometric polynomials of convex bodies associated to a given measure on the non-negative real line , which arise from the so called Wills functional. We study its structure, showing that the set of roots in the upper half-plane is a closed convex cone, containing the non-positive real axis , and strictly increasing in the dimension, for any measure . Moreover, it is proved that the 'smallest' cone of roots of these -polynomials is the one given by the Steiner polynomial, which provides, for example, additional information about the roots of -polynomials when the dimension is large enough. It will also give necessary geometric conditions for a sequence to be the moments of a certain measure on , a question regarding the so called (Stieltjes) moment problem.
Cite this article
María A. Hernández Cifre, Jesús Yepes Nicolás, On the roots of generalized Wills -polynomials. Rev. Mat. Iberoam. 31 (2015), no. 2, pp. 477–496DOI 10.4171/RMI/842