A theorem concerning approximation on the sphere

DOI10.1007/BF01989806zbMath0565.41033OpenAlexW1749663818MaRDI QIDQ1058690

P. I. Lizorkin, S. M. Nikol'skij

Publication date: 1983

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01989806

zbMATH Keywords

Laplace-Beltrami operatorspherical polynomialsapproximation on a unit sphere \(\sigma \)

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25)

Related Items (8)

Kolmogorov widths on the sphere via eigenvalue estimates for Hölderian integral operators ⋮ Essential rate for approximation by spherical neural networks ⋮ Unnamed Item ⋮ The direct and converse inequalities for Jackson-type operators on spherical cap ⋮ On approximation by reciprocals of spherical harmonics in \(L^p\) norm ⋮ On the best approximation of functions on the sphere in the metric of \(L_ p(S^ n), 1<p<{\infty}\) ⋮ Sharp constants of approximation theory. VI: weighted polynomial inequalities of different metrics on the multidimensional cube and ball ⋮ Equivalence of \(K\)-functional and modulus of smoothness of functions on the sphere

Cites Work

• Period, index and potential \(\text Ш\)
• On the finiteness of \(\text{ Ш}\) for motives associated to modular forms
• Lipschitz spaces on compact manifolds
• Über die Approximationsordnung bei Kugelfunktionen und algebraischen Polynomen
• Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten

This page was built for publication: A theorem concerning approximation on the sphere