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

Rafaela N. Bonfim ; Jean C. Guella ; Valdir A. Menegatto

Symmetry, integrability and geometry: methods and applications, Tome 14 (2018)

Résumé

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.

Détail

Keywords: strict positive definiteness; spheres; product kernels; linearization formulas; isotropy.

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