A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness

DOI10.1007/s00365-013-9217-zzbMath1284.41013arXiv1203.5157OpenAlexW1986343427MaRDI QIDQ387542

Josef Dick, Johann S. Brauchart

Publication date: 23 December 2013

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.5157

zbMATH Keywords

Sobolev spacesreproducing kernelspherical designsequal weight numerical integrationStolarsky's invariance principleWarnock's formula

Mathematics Subject Classification ID

Approximate quadratures (41A55) Approximation by other special function classes (41A30) Irregularities of distribution, discrepancy (11K38)

Related Items

Spherical $t_\epsilon $-designs for approximations on the sphere ⋮ A Riemann-Stein kernel method ⋮ Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold ⋮ Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness ⋮ Discrepancy and numerical integration on metric measure spaces ⋮ A non-linear approximation method on the sphere ⋮ Optimal \(N\)-point configurations on the sphere: ``magic numbers and Smale's 7th problem ⋮ Analyticity of Steklov eigenvalues of nearly circular and nearly spherical domains ⋮ Hyperuniform point sets on the sphere: deterministic aspects ⋮ Infinite-dimensional inverse problems with finite measurements ⋮ Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling ⋮ Distributing many points on spheres: minimal energy and designs

Uses Software

• DLMF

Cites Work

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