Differentiable Positive Definite Kernels on Spheres

DOI10.1515/JAA.2009.101zbMath1182.33021OpenAlexW2120607131MaRDI QIDQ3399038

Claudemir Pinheiro de Oliveira, Ana Paula Peron, Valdir A. Menegatto

Publication date: 29 September 2009

Published in: Journal of Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jaa.2009.101

zbMATH Keywords

spherical harmonicspositive definitenessdifferentiable kernelskernel expansionsdifferentiability of convergent series

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Positive definite functions in one variable harmonic analysis (42A82) Spherical harmonics (33C55) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (7)

Reproducing properties of differentiable Mercer-like kernels ⋮ Laplace-Beltrami differentiability of positive definite kernels on the sphere ⋮ Estimates on the derivatives and analyticity of positive definite functions on \(\mathbb{R}^m\) ⋮ Reproducing Properties of Differentiable Mercer-Like Kernels on the Sphere ⋮ Integral operators on the sphere generated by positive definite smooth kernels ⋮ Universal kernels which are continuous on the diagonal ⋮ Fundamental Sets of Functions on Locally Compact Abelian Groups

Cites Work

• Strictly positive definite kernels on subsets of the complex plane
• Integral operators on the sphere generated by positive definite smooth kernels
• Eigenvalues of integral operators with smooth positive definite kernels
• Positive definite matrices and differentiable reproducing kernel inequalities
• Eigenvalues of Positive Definite Kernels II
• Eigenvalues of Analytic Kernels
• Eigenvalues of Positive Definite Kernels
• Eigen-values of Lipschitz kernels
• Eigenvalues of Differentiable Positive Definite Kernels
• Term-by-Term Differentiability of Mercer's Expansion

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