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

Abstract

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.

References in corpus (7)

• Strictly and non-strictly positive definite functions on spheres
• Isotropic Gaussian random fields on the sphere: Regularity, fast simulation and stochastic partial differential equations
• An extension of a theorem of Schoenberg to products of spheres
• Strictly positive definite kernels on a product of circles
• Schoenberg's theorem for real and complex Hilbert spheres revisited
• Strictly Positive Definite Kernels on a Product of Spheres II
• Positive Definite Functions on Complex Spheres and their Walks through Dimensions

Cited by in corpus (2)

• Strictly positive definite kernels on the $2$-sphere: beyond radial symmetry
• A Note on the Derivatives of Isotropic Positive Definite Functions on the Hilbert Sphere