Über die Approximationsordnung bei Kugelfunktionen und algebraischen Polynomen

DOI10.2748/tmj/1178241489zbMath0243.41006OpenAlexW2094162145MaRDI QIDQ2554496

Siegfried Pawelke

Publication date: 1972

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178241489

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Multidimensional problems (41A63) Approximation by polynomials (41A10) Fourier series and coefficients in several variables (42B05) Spherical harmonics (33C55)

Related Items (32)

Exterior Dirichlet and Neumann problems and the linked ergodic inverse problems in the entire space ⋮ A fully discretised polynomial approximation on spherical shells ⋮ Bernstein inequality for differential operators ⋮ On the scientific work of Kunyang Wang ⋮ On the smoothness of the symbol of multidimensional singular integral operators ⋮ Best Polynomial Approximation on the Unit Sphere and the Unit Ball ⋮ Complexity of Monte Carlo integration for Besov classes on the unit sphere ⋮ Function approximation by deep networks ⋮ Laplace-Beltrami differentiability of positive definite kernels on the sphere ⋮ On quantities of the type of modulus of continuity and analogs of \(K\)-functionals in the spaces \(S^{(p,q)}(\sigma^{m-1})\) ⋮ Fourier-Laplace series on a sphere ⋮ Essential rate for approximation by spherical neural networks ⋮ Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis ⋮ Approximation and localized polynomial frame on conic domains ⋮ Quadrature in Besov spaces on the Euclidean sphere ⋮ Approximation with interpolatory constraints ⋮ A fully discretised filtered polynomial approximation on spherical shells ⋮ On the de la Vallée-Poussin means on the sphere ⋮ Local uniform error estimates for spherical basis functions interpolation ⋮ Galerkin approximation for elliptic PDEs on spheres ⋮ Direct and converse results in the \(Ba\) space for Jackson-Matsuoka polynomials on the unit sphere ⋮ Convergence for Summation Methods with Multipliers on the Sphere ⋮ Moduli of smoothness and approximation on the unit sphere and the unit ball ⋮ Generalized translation operator and approximation in several variables ⋮ On the representation of smooth functions on the sphere using finitely many bits ⋮ Inverse approximation theorems in the spaces \(S^{(p,q)}(\sigma^{m-1})\) ⋮ On the best approximation of functions on the sphere in the metric of \(L_ p(S^ n), 1<p<{\infty}\) ⋮ Old and New on the Laplace-Beltrami Derivative ⋮ Discretized Newman-Shapiro operators and Jackson's inequality on the sphere ⋮ Central approximation processes ⋮ A theorem concerning approximation on the sphere ⋮ Equivalence of \(K\)-functional and modulus of smoothness of functions on the sphere

Cites Work

• Interpolation in polynomial classes and Markoff's inequality
• Approximation theorems connected with generalized translations
• Derivatives of a polynomial of best approximation
• On the fundamental approximation theorems of D. Jackson, S.N. Bernstein and theorems of M. Zamansky and S.B. Stechkin
• Über Sätze von M. Zamansky und S.B. Steckin und ihre Umkehrungen auf dem \(n\)-dimensionalen Torus
• Smooth functions
• Classes de saturation de certains procédés d'approximation des séries de Fourier des fonctions continues et applications à quelques problèmes d'approximation
• On a Problem of Mihlin
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