Schoenberg coefficients and curvature at the origin of continuous isotropic positive definite kernels on spheres

DOI10.1016/j.spl.2019.108618zbMath1456.42007arXiv1807.02363OpenAlexW2973019176WikidataQ127243582 ScholiaQ127243582MaRDI QIDQ2288767

Ahmed Arafat, Emilio Porcu, Pablo Gregori

Publication date: 20 January 2020

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.02363

zbMATH Keywords

Gegenbauer polynomialspositive definite kernelSchoenberg coefficientsisotropic covariance function

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Positive definite functions in one variable harmonic analysis (42A82) Integral equations with miscellaneous special kernels (45H05)

Related Items

Relations between Schoenberg coefficients on real and complex spheres of different dimensions ⋮ Series expansions among weighted Lebesgue function spaces and applications to positive definite functions on compact two-point homogeneous spaces ⋮ The turning arcs: a computationally efficient algorithm to simulate isotropic vector-valued Gaussian random fields on the \(d\)-sphere ⋮ A note on the derivatives of isotropic positive definite functions on the Hilbert sphere

Uses Software

• DLMF

Cites Work

• An extension of a theorem of Schoenberg to products of spheres
• Strictly positive definite kernels on a product of spheres. II.
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• Differentiability of bizonal positive definite kernels on complex spheres
• Covariance functions on spheres cross time: beyond spatial isotropy and temporal stationarity
• Generalized convolution roots of positive definite kernels on complex spheres
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• Positive definite functions on spheres
• Derivatives of isotropic positive definite functions on spheres
• Positive definite functions on the unit sphere and integrals of Jacobi polynomials
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• Dimension walks and Schoenberg spectral measures
• A Polya criterion for (strict) positive-definiteness on the sphere
• Convolution roots and differentiability of isotropic positive definite functions on spheres
• Modeling Temporally Evolving and Spatially Globally Dependent Data

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