Strictly Positive Definite Kernels on a Product of Spheres II

Abstract

We present, among other things, a necessary and sufficient condition for the strict positive definiteness of an isotropic and positive definite kernel on the cartesian product of a circle and a higher dimensional sphere. The result complements similar results previously obtained for strict positive definiteness on a product of circles [Positivity, to appear, arXiv:1505.01169] and on a product of high dimensional spheres [J. Math. Anal. Appl. 435 (2016), 286-301, arXiv:1505.03695].

References in corpus (7)

• An extension of a theorem of Schoenberg to products of spheres
• Strictly positive definite kernels on a product of circles
• Strictly positive definite kernels on two-point compact homogeneous spaces
• One-Step Recurrences for Stationary Random Fields on the Sphere
• Dimension hopping and families of strictly positive definite zonal basis functions on spheres
• Strict positive definiteness on a product of compact two-point homogeneous spaces
• From Schoenberg coefficients to Schoenberg functions

Cited by in corpus (4)

• Relations between Schoenberg Coefficients on Real and Complex Spheres of Different Dimensions
• Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative
• Characterization of Strict Positive Definiteness on products of complex spheres
• A Gneiting-Like Method for Constructing Positive Definite Functions on Metric Spaces