Schoenberg's theorem for real and complex Hilbert spheres revisited

DOI10.1016/j.jat.2018.02.003zbMath1388.43006arXiv1701.07214OpenAlexW2581972952MaRDI QIDQ1704133

Emilio Porcu, Ana Paula Peron, Christian Berg

Publication date: 8 March 2018

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.07214

zbMATH Keywords

Gegenbauer polynomialspositive definite functionsdisc polynomialsspherical harmonics for real and complex spheres

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Spherical harmonics (33C55) Positive definite functions on groups, semigroups, etc. (43A35)

Related Items (8)

Multivariate Gaussian Random Fields over Generalized Product Spaces involving the Hypertorus ⋮ Relations between Schoenberg coefficients on real and complex spheres of different dimensions ⋮ Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces ⋮ A Gneiting-like method for constructing positive definite functions on metric spaces ⋮ Dimension walks on \(\mathbb{S}^d \times \mathbb{R}\) ⋮ A note on the derivatives of isotropic positive definite functions on the Hilbert sphere ⋮ Characterization of strict positive definiteness on products of complex spheres ⋮ Pólya-type criteria for conditional strict positive definiteness of functions on spheres

Cites Work

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• Strictly and non-strictly positive definite functions on spheres
• From Schoenberg coefficients to Schoenberg functions
• Inequalities for Jacobi polynomials
• Positive definite kernels on the complex Hilbert sphere
• Positive definite functions on complex spheres and their walks through dimensions
• Generalized Zernike or disc polynomials
• Differentiability of bizonal positive definite kernels on complex spheres
• Determinantal point process models on the sphere
• Spherical harmonics
• Positive definite functions on spheres
• Convolution roots and differentiability of isotropic positive definite functions on spheres
• Positive definite kernels on complex spheres

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