A characterization of dual quermassintegrals and the roots of dual Steiner polynomials

It turns out that the characterization of dual quermassintegrals is related to the moment problem, and based on this relation, we also derive new determinantal inequalities among the dual quermassintegrals. Moreover, this characterization will be the key tool in order to investigate structural properties of the set of roots of dual Steiner polynomials of star bodies.