Strictly positive definite kernels on two-point compact homogeneous spaces
Functional Analysis
2015-10-20 v2
Abstract
We present a necessary and sufficient condition for the strict positive definiteness of a real, continuous, isotropic and positive definite kernel on a two-point compact homogeneous space. The characterization adds to others previously obtained by D. Chen at all (2003) in the case in which the space is a sphere of dimension at least 2 and Menegatto at all (2006) in the case in which the space is the unit circle. As an application, we use the characterization to improve upon a recent result on the differentiability of positive definite kernels on the spaces.
Cite
@article{arxiv.1505.00591,
title = {Strictly positive definite kernels on two-point compact homogeneous spaces},
author = {V. S. Barbosa and V. A. Menegatto},
journal= {arXiv preprint arXiv:1505.00591},
year = {2015}
}