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arXiv · 1803.03105

Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative

Rafaela N. Bonfim·Jean C. Guella·Valdir A. Menegatto
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Abstract

For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a similar characterization for kernels on the space-time setting $G \times S^d$, where $G$ is a locally compact group and $S^d$ is the unit sphere in $\mathbb{R}^{d+1}$, keeping isotropy of the kernels with respect to the $S^d$ component. Among other things, these results provide new procedures for the construction of valid models for interpolation and approximation on compact two-point homogeneous spaces.

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Rafaela N. Bonfim, Jean C. Guella, Valdir A. Menegatto. 2018-02-22. Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative. https://doi.org/10.3842/sigma.2018.112

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