Projections of orbital measures for classical Lie groups

In this paper we compute the radial parts of projections of the orbital measures for the compact Lie groups $SO(2n+1),Sp(2n)$ and $O(2n)$, extending the previous results for the case of the unitary group by Olshanski and Faraut. The answer is given in terms of determinants of the B-splines with the knots arranged symmetrically about zero.