Strictly positive definite kernels on compact Riemannian manifolds

TL;DR

This paper establishes new conditions for strictly positive definite kernels on compact Riemannian manifolds, including product spaces, enhancing understanding of kernel properties in geometric contexts.

Contribution

It introduces novel criteria for strict positive definiteness of kernels on general and convolutional structures on compact Riemannian manifolds and their products.

Findings

New conditions for strict positive definiteness on general kernels

Conditions for kernels with convolutional structure

Criteria for kernels on product manifolds, including two-point homogeneous spaces

Abstract

The paper studies strictly positive definite kernels on compact Riemannian manifolds. We state new conditions to ensure strict positive definiteness for general kernels and kernels with certain convolutional structure. We also state conditions for such kernels on product manifolds. As an example conditions for products of two-point homogeneous spaces are presented.