Laplace-Beltrami differentiability of positive definite kernels on the sphere

DOI10.1007/s10114-012-1067-2zbMath1268.33010OpenAlexW2075703011MaRDI QIDQ1942651

Mario Castro, Valdir A. Menegatto, Claudemir P. Oliveira

Publication date: 19 March 2013

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-012-1067-2

zbMATH Keywords

positive definite kernelsspherical harmonicsLaplace-Beltrami operatoranalysis on spheres

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Positive definite functions in one variable harmonic analysis (42A82) Spherical harmonics (33C55) Harmonic analysis and spherical functions (43A90) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (3)

Reproducing properties of differentiable Mercer-like kernels ⋮ Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere ⋮ Schoenberg coefficients and curvature at the origin of continuous isotropic positive definite kernels on spheres

Cites Work

• Integral operators on the sphere generated by positive definite smooth kernels
• Approximation theory on the sphere
• Multivariate polynomial approximation
• Error bounds for solving pseudodifferential equations on spheres by collocation with zonal kernels
• Über die Approximationsordnung bei Kugelfunktionen und algebraischen Polynomen
• Eigenvalue decay of positive integral operators on the sphere
• Old and New on the Laplace-Beltrami Derivative
• Differentiable Positive Definite Kernels on Spheres
• Spherical Harmonics
• Uniqueness Theory for Laplace Series
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Laplace-Beltrami differentiability of positive definite kernels on the sphere