A scheme for interpolation by Hankel translates of a basis function

DOI10.1016/j.jat.2012.08.005zbMath1262.41001OpenAlexW1990580282MaRDI QIDQ692565

Isabel Marrero, Cristian Arteaga

Publication date: 6 December 2012

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

Full work available at URL: https://doi.org/10.1016/j.jat.2012.08.005

zbMATH Keywords

Hankel translationSobolev embedding theoremBessel operatorBessel-Kingman hypergroupbasis functionHankel convolutionminimal norm interpolant

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Interpolation in approximation theory (41A05) Approximation by other special function classes (41A30)

Related Items

Density in spaces of interpolation by Hankel translates of a basis function, The role of nonpolynomiality in uniform approximation by RBF networks of Hankel translates, Direct form seminorms arising in the theory of interpolation by Hankel translates of a basis function, Universal approximation by radial basis function networks of Delsarte translates, Radially symmetric thin plate splines interpolating a circular contour map, Radial basis function neural networks of Hankel translates as universal approximators, Approximation in weighted \(p\)-mean by RBF networks of Delsarte translates, Wiener's tauberian theorems for the Fourier-Bessel transformation and uniform approximation by RBF networks of Delsarte translates

Uses Software

• Matlab

Cites Work

• Decomposition of conditionally positive definite functions on commutative hypergroups
• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Variation diminishing Hankel transforms
• Spaces of distributions, interpolation by translates of a basis function and error estimates
• Operators on radial functions
• A Duchon framework for the sphere
• \(L_{p}\)-error estimates for radial basis function interpolation on the sphere
• McKennon-type spaces for the Hankel transformation
• Random walks with spherical symmetry
• Metric spaces and completely monontone functions
• Les espaces du type de Beppo Levi
• A Generalised Hankel Convolution
• Local error estimates for radial basis function interpolation of scattered data
• Sur l’erreur d’interpolation des fonctions de plusieurs variables par les $D^m$-splines
• The Hankel Convolution and the Zemanian Spaces β_μ and β'_μ
• Radial Basis Functions
• Regular and absolutely regular Hankel-transformable distributions
• Multivariate Interpolation and Conditionally Positive Definite Functions. II
• Integral Equations Associated with Hankel Convolutions
• A Hankel convolution complex inversion theory
• A Distributional Hankel Transformation
• The Hankel Transformation of Certain Distributions of Rapid Growth
• A necessary and sufficient condition for the representation of a function as a Hankel-Stieltjes transform
• The Structure of the Algebra of Hankel Transforms and the Algebra of Hankel-Stieltjes Transforms
• On Functions Positive Definite Relative to the Orthogonal Group and the Representation of Functions as Hankel-Stieltjes Transforms
• Metric Spaces and Positive Definite Functions
• Scattered Data Approximation
• Transference for hypergroups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item