  For any $I\subset\mathbb{R}$ finite with $0\in I$, we provide a
characterization of those tuples $(\omega_i)_{i\in I}$ of positive numbers
which are dual querma\ss integrals of two star bodies. It turns out that this
problem is related to the moment problem. Based on this relation we also get
new inequalities for the dual querma\ss integrals. Moreover, the above
characterization will be the key tool in order to investigate structural
properties of the set of roots of dual Steiner polynomials of star bodies.
