Strict positive definiteness on products of compact two-point homogeneous spaces

DOI10.1080/10652469.2016.1249867zbMath1361.42027arXiv1605.07071OpenAlexW2396206955MaRDI QIDQ2968809

V. S. Barbosa, Valdir A. Menegatto

Publication date: 22 March 2017

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.07071

zbMATH Keywords

Jacobi polynomialsGauss hypergeometric functionisotropytwo point homogeneous spaces

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Classical hypergeometric functions, ({}_2F_1) (33C05) Spherical harmonics (33C55)

Related Items (14)

Strictly positive definite functions on compact two-point homogeneous spaces: the product alternative ⋮ Relations between Schoenberg coefficients on real and complex spheres of different dimensions ⋮ Strictly positive definite kernels on a product of spheres. II. ⋮ Equivalence and orthogonality of Gaussian measures on spheres ⋮ Series expansions among weighted Lebesgue function spaces and applications to positive definite functions on compact two-point homogeneous spaces ⋮ Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces ⋮ Modeling Temporally Evolving and Spatially Globally Dependent Data ⋮ Strictly positive definite non-isotropic kernels on two-point homogeneous manifolds: the asymptotic approach ⋮ A limit formula for semigroups defined by Fourier-Jacobi series ⋮ Positive definite functions on products of metric spaces via generalized Stieltjes functions ⋮ A Gneiting-like method for constructing positive definite functions on metric spaces ⋮ Towards a complete picture of stationary covariance functions on spheres cross time ⋮ Regularity and approximation of Gaussian random fields evolving temporally over compact two-point homogeneous spaces ⋮ Characterization of strict positive definiteness on products of complex spheres

Cites Work

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• An extension of a theorem of Schoenberg to products of spheres
• Strictly and non-strictly positive definite functions on spheres
• From Schoenberg coefficients to Schoenberg functions
• Localization of spherical harmonic expansions
• Strictly positive definite kernels on a product of spheres
• The addition formula for the eigenfunctions of the Laplacian
• Strictly positive definite kernels on a product of circles
• Two-point homogeneous spaces
• Positive definite functions on spheres
• The Addition Formula for Jacobi Polynomials and Spherical Harmonics

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