Relations between Schoenberg Coefficients on Real and Complex Spheres of Different Dimensions

Abstract

Positive definite functions on spheres have received 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 recent 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 by describing an application to strict positive definiteness.