Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness
DOI10.1007/978-3-319-72456-0_9zbMath1405.65076OpenAlexW2803872864MaRDI QIDQ4611799
Publication date: 22 January 2019
Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-319-72456-0_9
General theory of numerical analysis in abstract spaces (65J05) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)
Related Items (1)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Optimal asymptotic bounds for spherical designs
- A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness
- Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\)
- Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces
- Computational existence proofs for spherical \(t\)-designs
- Filtered hyperinterpolation: a constructive polynomial approximation on the sphere
- Numerical integration over spheres of arbitrary dimension
- Optimal recovery of Besov classes of generalized smoothness and Sobolev classes on the sphere
- A variational characterisation of spherical designs
- Spherical codes and designs
- Asymptotik bei Jacobi-Polynomen und Jacobi-Funktionen
- Fully symmetric interpolatory rules for multiple integrals over hyper-spherical surfaces
- Extremal systems of points and numerical integration on the sphere
- Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling
- A lower bound for the worst-case cubature error on spheres of arbitrary dimension
- Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order
- Spherical harmonics
- Optimal lower bounds for cubature error on the sphere \(S^2\)
- Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
- FILTERED POLYNOMIAL APPROXIMATION ON THE SPHERE
- A simple proof of Stolarsky’s invariance principle
- Regularized Least Squares Approximations on the Sphere Using Spherical Designs
- Well Conditioned Spherical Designs for Integration and Interpolation on the Two-Sphere
- QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
- A Uniform Asymptotic Expansion of the Jacobi Polynomials with Error Bounds
- Multivariate interpolation of large sets of scattered data
- A generalized discrepancy and quadrature error bound
- Worst-case errors in a Sobolev space setting for cubature over the sphere S2
- Sums of Distances Between Points on a Sphere. II
- One-bit sensing, discrepancy and Stolarsky's principle
- Existence of Solutions to Systems of Underdetermined Equations and Spherical Designs
- Integrals with nearly coincident branch points: Gegenbauer polynomials of large degree
- Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten
This page was built for publication: Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness
