DOI10.1090/S0025-5718-00-01240-0zbMath0980.76070OpenAlexW1981867435MaRDI QIDQ2719068
Francis J. Narcowich, Hrushikesh N. Mhaskar, Joseph D. Ward
Publication date: 14 May 2001
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-00-01240-0
Kolmogorov width of classes of smooth functions on the sphere \(\mathbb S^{d-1}\),
Greedy algorithm with regard to the needlet system on the sphere,
Zooming from global to local: a multiscale RBF approach,
Local quadrature formulas on the sphere,
Sampling discretization and related problems,
Nonparametric regression using needlet kernels for spherical data,
Decomposition of Besov and Triebel-Lizorkin spaces on the sphere,
Asymptotically optimal designs on compact algebraic manifolds,
Distributed learning via filtered hyperinterpolation on manifolds,
Optimal asymptotic bounds for spherical designs,
Probabilistic Marcinkiewicz-Zygmund inequalities on the rotation group,
Marcinkiewicz-Zygmund inequalities,
Radial basis function approximation of noisy scattered data on the sphere,
Local Approximation Using Hermite Functions,
Spherical random sampling of localized functions on 𝕊ⁿ⁻¹,
A Plancherel-Polya inequality in Besov spaces on spaces of homogeneous type,
Direct approximation on spheres using generalized moving least squares,
Optimal recovery of Besov classes of generalized smoothness and Sobolev classes on the sphere,
Cubature formula for spherical basis function networks,
Uniform approximation on the sphere by least squares polynomials,
Marcinkiewicz-Zygmund inequalities and the numerical approximation of singular integrals for exponential weights: Methods, results and open problems, some new, some old,
On the reconstruction of functions from values at subsampled quadrature points,
Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere,
Optimal cubature formulas in weighted Besov spaces with \(A _{\infty }\) weights on multivariate domains,
Local approximation of operators,
Sketching with Spherical Designs for Noisy Data Fitting on Spheres,
Is hyperinterpolation efficient in the approximation of singular and oscillatory functions?,
Widths of Besov classes of generalized smoothness on the sphere,
Marcinkiewicz-Zygmund type results in multivariate domains,
Needlet-Whittle estimates on the unit sphere,
On the stability of unevenly spaced samples for interpolation and quadrature,
The needlets bispectrum,
Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness,
Entropy numbers of Besov classes of generalized smoothness on the sphere,
A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel,
Numerical integration with polynomial exactness over a spherical cap,
Spectral estimation on the sphere with needlets: high frequency asymptotics,
Phase retrieval using random cubatures and fusion frames of positive semidefinite matrices,
Marcinkiewicz-Zygmund measures on manifolds,
Gaussian semiparametric estimates on the unit sphere,
Marcinkiewicz–Zygmund Inequalities and Polynomial Approximation from Scattered Data onSO(3),
Kernel based quadrature on spheres and other homogeneous spaces,
Marcinkiewicz-Zygmund inequalities and interpolation by spherical polynomials with respect to doubling weights,
On Marcinkiewicz-Zygmund Inequalities at Hermite Zeros and Their Airy Function Cousins,
Local numerical integration on the sphere,
Marcinkiewicz-Zygmund inequalities and interpolation by spherical harmonics,
Sufficient conditions for sampling and interpolation on the sphere,
On spherical harmonics based numerical quadrature over the surface of a sphere,
Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis,
An inverse theorem for compact Lipschitz regions in ℝ^{𝕕} using localized kernel bases,
Approximation and localized polynomial frame on conic domains,
Tikhonov regularization for polynomial approximation problems in Gauss quadrature points,
Quadrature in Besov spaces on the Euclidean sphere,
Approximation with interpolatory constraints,
Needlet approximation for isotropic random fields on the sphere,
Cubature Formulas and Discrete Fourier Transform on Compact Manifolds,
The convergence rate for a \(K\)-functional in learning theory,
Quadrature formulas for integration of multivariate trigonometric polynomials on spherical triangles,
A unified approach to scattered data approximation on \(\mathbb{S}^{\mathbf {3}}\) and \(\mathrm{SO(3)}\),
Well-separated spherical designs,
Galerkin approximation for elliptic PDEs on spheres,
On the representation of band limited functions using finitely many bits,
Complexity of numerical integration over spherical caps in a Sobolev space setting,
$L^p$ Bernstein estimates and approximation by spherical basis functions,
Multivariate polynomial inequalities with respect to doubling weights and \(A_{\infty}\) weights,
Fast evaluation of quadrature formulae on the sphere,
Positive cubature formulas and Marcinkiewicz-Zygmund inequalities on spherical caps,
Weighted quadrature formulas and approximation by zonal function networks on the sphere,
Approximation of smooth functions on compact two-point homogeneous spaces,
On the representation of smooth functions on the sphere using finitely many bits,
Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order,
Tight framelets and fast framelet filter bank transforms on manifolds,
Sampling, splines and frames on compact manifolds,
Polynomial operators for spectral approximation of piecewise analytic functions,
Irregular sampling of band-limited functions on the sphere,
Marcinkiewicz-Zygmund inequalities for polynomials in Bergman and Hardy spaces,
Optimal Monte Carlo integration on closed manifolds,
On the positivity and magnitudes of Bayesian quadrature weights,
A note on stability results for scattered data interpolation on Euclidean spheres,
Probabilistic spherical Marcinkiewicz-Zygmund inequalities,
On the computation of nonnegative quadrature weights on the sphere,
Polynomial inequalities in Lebesgue spaces with variable exponents on the sphere,
Hyperuniform point sets on the sphere: probabilistic aspects,
Sampling, Marcinkiewicz-Zygmund inequalities, approximation, and quadrature rules,
Characterizations of function spaces on the sphere using frames,
Ridge wavelets on the ball,
Distributed Filtered Hyperinterpolation for Noisy Data on the Sphere,
Parameter Choice Strategies for Least-squares Approximation of Noisy Smooth Functions on the Sphere,
Quasi-interpolation in shift invariant spaces,
Optimal lower bounds for cubature error on the sphere \(S^2\),
On the quadrature exactness in hyperinterpolation