Approximation in rough native spaces by shifts of smooth kernels on spheres

DOI10.1016/j.jat.2004.12.005zbMath1082.41018OpenAlexW2089288976MaRDI QIDQ1772706

Jeremy Levesley, Xingping Sun

Publication date: 21 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.jat.2004.12.005

zbMATH Keywords

harmonic polynomialsreproducing kernelsradial basis functionnative space

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) General harmonic expansions, frames (42C15) Interpolation in approximation theory (41A05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Spherical harmonics (33C55) Approximation by other special function classes (41A30)

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Linear and nonlinear approximation of spherical radial basis function networks, Scattered data quasi‐interpolation on spheres, Perturbed kernel approximation on homogeneous manifolds, Multiscale interpolation on the sphere: convergence rate and inverse theorem, Jackson-type inequalities for spherical neural networks with doubling weights, Cubature formula for spherical basis function networks, Spherical basis functions and uniform distribution of points on spheres, On approximation by spherical reproducing kernel Hilbert spaces, Sketching with Spherical Designs for Noisy Data Fitting on Spheres, A general radial quasi-interpolation operator on the sphere, Local uniform error estimates for spherical basis functions interpolation, Spherical data fitting by multiscale moving least squares, Convergence for Summation Methods with Multipliers on the Sphere, Interpolation and best approximation for spherical radial basis function networks, Error and stability estimates for surface-divergence free RBF interpolants on the sphere, L^pError Estimates for Scattered Data Interpolation On Spheres, Spherical scattered data quasi-interpolation by Gaussian radial basis function

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