Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold
DOI10.1007/s00365-023-09638-0arXiv1909.12334OpenAlexW2976107918MaRDI QIDQ6101227
Josef Dick, Christian Krattenthaler, Manuel Gräf, Martin Ehler
Publication date: 20 June 2023
Published in: Constructive Approximation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1909.12334
Euclidean ballspecial orthogonal groupnonequispaced fast Fourier transformspectral decompositionsGrassmannian manifolddiscrepancy kernels
Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Harmonic analysis on homogeneous spaces (43A85) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Numerical methods for discrete and fast Fourier transforms (65T50) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Convergence of probability measures (60B10) Numerical methods for trigonometric approximation and interpolation (65T40)
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Cites Work
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- A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness
- Boundary conditions for the volume potential for the polyharmonic equation
- A projection method on measures sets
- On the convergence of expansions in polyharmonic eigenfunctions
- On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms
- Weighted geometric discrepancies and numerical integration on reproducing kernel Hilbert spaces
- Points on manifolds with asymptotically optimal covering radius
- Tractability of multivariate problems. Volume II: Standard information for functionals.
- A fast algorithm for nonequispaced Fourier transforms on the rotation group
- On the operator \(\Delta r^2 + \mu (\partial/\partial r) r + \lambda\)
- Generalized sums of distances
- Radial positive definite functions generated by Euclid's hat
- Spherical functions on the Grassmann manifold and generalized Jacobi polynomials. 2
- Fast spherical Fourier algorithms.
- Codes and designs in Grassmannian spaces.
- Elliptic partial differential equations of second order
- Asymptotically optimal designs on compact algebraic manifolds
- Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians
- Designs in Grassmannian spaces and lattices
- Bounds for codes and designs in complex subspaces
- Stolarsky's invariance principle for projective spaces
- Spectral Theory for Gaussian Processes: Reproducing Kernels, Boundaries, and L2-Wavelet Generators with Fractional Scales
- A simple proof of Stolarsky’s invariance principle
- On a generalization of the generating function for Gegenbauer polynomials
- Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates
- Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
- Sampling Sets and Quadrature Formulae on the Rotation Group
- QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
- Linear programming bounds for codes in grassmannian spaces
- Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians
- Packing Lines, Planes, etc.: Packings in Grassmannian Spaces
- Generalized Jacobi Polynomials as Spherical Functions of the Grassmann Manifold
- Quadrature Errors, Discrepancies, and Their Relations to Halftoning on the Torus and the Sphere
- Quadrature rules and distribution of points on manifolds
- The fundamental solution of linear elliptic differential equations with analytic coefficients
- Optimal Transport Approximation of 2-Dimensional Measures
