  Positive definite functions on spheres have received an increasing interest
in many branches of mathematics and statistics. In particular, the Schoenberg
sequences in the spectral representation of positive definite functions have
been studied by several mathematicians in the last years. This paper provides a
set of relations between Schoenberg sequences defined over real as well as
complex spheres of different dimensions. We illustrate our findings describing
an application to strict positive definiteness.
