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This article is cited in 3 scientific papers (total in 3 papers)
Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative
Rafaela N. Bonfima, Jean C. Guellab, Valdir A. Menegattob a DEMAT-Universidade Federal de São João Del Rei, Praça Frei Orlando, 170, Centro, 36307-352 São João del Rei - MG, Brazil
b Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos - SP, Brazil
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.
Keywords:
strict positive definiteness; spheres; product kernels; linearization formulas; isotropy.
Received: March 8, 2018; in final form October 10, 2018; Published online October 16, 2018
Citation:
Rafaela N. Bonfim, Jean C. Guella, Valdir A. Menegatto, “Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative”, SIGMA, 14 (2018), 112, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1411 https://www.mathnet.ru/eng/sigma/v14/p112
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Abstract page: | 127 | Full-text PDF : | 23 | References: | 20 |
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