The best approximation of the classes of functions \(W_ p^{\alpha}(S^ n)\) by polynomials in spherical harmonics

DOI10.1007/BF01140192zbMath0538.42011MaRDI QIDQ793262

A. I. Kamzolov

Publication date: 1983

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

spherical harmonicsLaplace-Beltrami operatorbest approximationhomogeneous harmonic polynomials

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Multidimensional problems (41A63) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)

Related Items (6)

Kolmogorov width of classes of smooth functions on the sphere \(\mathbb S^{d-1}\) ⋮ Widths of Besov classes of generalized smoothness on the sphere ⋮ On the existence and uniqueness of solution to problems of fluid dynamics on a sphere ⋮ Approximation of smooth functions on compact two-point homogeneous spaces ⋮ Estimates for \(n\)-widths of sets of smooth functions on complex spheres ⋮ Theory of deep convolutional neural networks. II: Spherical analysis

Cites Work

• On the behavior of special classes of ultraspherical expansions. I, II
• Unnamed Item

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