Dimension walks on $\mathbb{S}^d \times \mathbb{R}$

TL;DR

This paper extends known recurrence relations for positive definite functions from spheres to the combined space of spheres and real numbers, addressing the spatio-temporal case.

Contribution

It demonstrates that existing recurrences for positive definite functions on spheres also apply to the spatio-temporal setting, broadening their applicability.

Findings

Recurrences for positive definite functions are valid in the spatio-temporal context.

Extension from spheres to $ imes \, \mathbb{R}$ is verified.

Supports analysis of spatio-temporal processes on spherical domains.

Abstract

We verify that the established one- and two-step recurrences for positive definite functions on spheres extend to the spatio-temporal case.