Conditional limiting distribution of beta-independent random vectors

The paper deals with random vectors X in Rd,d≥2Rd,d≥2, possessing the stochastic representation X=dARV, where RR is a positive random radius independent of the random vector V and A∈Rd×dA∈Rd×d is a non-singular matrix. If V is uniformly distributed on the unit sphere of RdRd, then for any integer m