Probability, Statistics and Planet Earth, II:The Bochner-Godement theorem for symmetric spaces

TL;DR

This paper extends the Bochner-Godement theorem to general symmetric spaces, unifying several recent results and exploring their applications in harmonic analysis on these spaces.

Contribution

It generalizes the Bochner-Godement theorem to symmetric spaces, encompassing recent product space results and discussing their implications.

Findings

Unified framework for harmonic analysis on symmetric spaces

Inclusion of recent product space theorems

Discussion of applications in related fields

Abstract

The Bochner-Godement theorem extends the classical Bochner and Bochner-Schoenberg theorems from the context of Euclidean spaces and spheres to general symmetric spaces. We show how it also includes recent results on products of symmetric spaces: the Berg-Porcu theorem (sphere cross line), and the Guella-Menegatto-Peron theorem (products of spheres), and discuss related results and applications.