$L^p$ Bernstein estimates and approximation by spherical basis functions
From MaRDI portal
Publication:3584842
DOI10.1090/S0025-5718-09-02322-9zbMath1200.41019arXiv0810.5075MaRDI QIDQ3584842
Joseph D. Ward, Jürgen Prestin, Francis J. Narcowich, Hrushikesh N. Mhaskar
Publication date: 30 August 2010
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0810.5075
Related Items
Linear and nonlinear approximation of spherical radial basis function networks, Nonparametric regression using needlet kernels for spherical data, Green’s Functions: Taking Another Look at Kernel Approximation, Radial Basis Functions, and Splines, Graph signal interpolation with positive definite graph basis functions, Fully discrete needlet approximation on the sphere, Polyharmonic and related kernels on manifolds: interpolation and approximation, Eigenvalue Sequences of Positive Integral Operators and Moduli of Smoothness, Generalised Wendland functions for the sphere, A Petrov--Galerkin Kernel Approximation on the Sphere, Equidistributed icosahedral configurations on the sphere, Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds, \(L^p\) error estimates for approximation by Sobolev splines and Wendland functions on \(\mathbb R^d\), Minimum Sobolev norm interpolation with trigonometric polynomials on the torus, Kernel based quadrature on spheres and other homogeneous spaces, Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis, Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces, An inverse theorem for compact Lipschitz regions in ℝ^{𝕕} using localized kernel bases, A high-order meshless Galerkin method for semilinear parabolic equations on spheres, Needlet approximation for isotropic random fields on the sphere, Regularized kernel-based reconstruction in generalized Besov spaces, Cubature Formulas and Discrete Fourier Transform on Compact Manifolds, \(L^p\) Bernstein inequalities and inverse theorems for RBF approximation on \(\mathbb{R}^d\), Interpolation and best approximation for spherical radial basis function networks, A novel Galerkin method for solving PDES on the sphere using highly localized kernel bases, Numerical computation of triangular complex spherical designs with small mesh ratio
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multiscale potential theory. With applications to geoscience
- Decomposition of Besov and Triebel-Lizorkin spaces on the sphere
- The analysis of linear partial differential operators. III: Pseudo-differential operators
- Approximation power of RBFs and their associated SBFs: a connection
- Analysis of the Laplacian on a complete Riemannian manifold
- Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds
- Equivalence of \(K\)-functional and modulus of smoothness of functions on the sphere
- A survey on spherical spline approximation
- On the representation of smooth functions on the sphere using finitely many bits
- Approximation properties of zonal function networks using scattered data on the sphere
- Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions
- Localized polynomial frames on the ball
- Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere
- Weighted quadrature formulas and approximation by zonal function networks on the sphere
- Spherical harmonics
- Positive definite functions on spheres
- Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
- Inverse and saturation theorems for radial basis function interpolation
- Characterizations of function spaces on the sphere using frames
- Localized Tight Frames on Spheres
- Ten Lectures on Wavelets
- Strictly positive definite functions on spheres in Euclidean spaces
- Scattered Data Interpolation on Spheres: Error Estimates and Locally Supported Basis Functions
- Scattered Data Approximation
- Polynomial frames on the sphere
