Isotropic positive definite functions on spheres generated from those in Euclidean spaces

DOI10.1090/proc/14454zbMath1426.33031OpenAlexW2899615934MaRDI QIDQ5384828

Zhihui Nie, Chunsheng Ma

Publication date: 26 June 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10057/16383

zbMATH Keywords

sphereBessel functionpositive definite functionJacobi polynomialultraspherical polynomialcompactly support function

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Positive definite functions in one variable harmonic analysis (42A82) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (6)

Strict positive definiteness of convolutional and axially symmetric kernels on \(d\)-dimensional spheres ⋮ Compactly-supported isotropic covariances on spheres obtained from matrix-valued covariances in Euclidean spaces ⋮ Isotropic positive definite functions on spheres ⋮ A note on the derivatives of isotropic positive definite functions on the Hilbert sphere ⋮ Pólya-type criteria for conditional strict positive definiteness of functions on spheres ⋮ Isotropic covariance matrix functions on compact two-point homogeneous spaces

Uses Software

• Matlab
• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Excursion probability of Gaussian random fields on sphere
• Time varying isotropic vector random fields on spheres
• Metric spaces and completely monontone functions
• Positive definite functions on spheres
• Stochastic representations of isotropic vector random fields on spheres
• Isotropic covariance matrix polynomials on spheres
• Positive Sums of the Classical Orthogonal Polynomials
• Positive definite functions on the unit sphere and integrals of Jacobi polynomials
• A necessary and sufficient condition for strictly positive definite functions on spheres
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• A Polya criterion for (strict) positive-definiteness on the sphere
• Fourier Transforms. (AM-19)

This page was built for publication: Isotropic positive definite functions on spheres generated from those in Euclidean spaces