Full length article: New moduli of smoothness on the unit ball, applications and computability
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TL;DR: The usefulness of these moduli of smoothness on the unit ball is demonstrated here by some applications and the optimality of the conditions in some theorems as well as the computability of the moduli are exhibited.
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About: This article is published in Journal of Approximation Theory. The article was published on 01 Mar 2014. and is currently open access. The article focuses on the topics: Moduli of algebraic curves & Modular equation.
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References
Moduli of smoothness and approximation on the unit sphere and the unit ball
TL;DR: In this paper, a new modulus of smoothness based on the Euler angles is introduced on the unit sphere and is shown to satisfy all the usual characteristic properties of moduli of smootness, including direct and inverse theorem for the best approximation by polynomials and its equivalence to a K-functional, defined via partial derivatives in Euler angle.
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A modulus of smoothness on the unit sphere
TL;DR: In this article, the authors define new simple moduli of smoothness for functions on the unit sphere inR676 d−1 (the unit sphere of R676 d) and, in particular, for functions for f ∈ L petertodd p(S petertodd d −1) and for f∈ L676 p (S�� d − 1) for functions over R676d.
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Weak Type Estimates for Cesaro Sums of Jacobi Polynomial Series
Sagun Chanillo,Benjamin Muckenhoupt +1 more
- 01 Jun 1993
TL;DR: In this paper, an absolute value estimate for $3(1-y)-leq 2( 1-x)$ and a basic estimate for ε(1)-approximation for separated arguments is given.
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Optimal Cubature Formulas in Weighted Besov Spaces with A ∞ Weights on Multivariate Domains
Feng Dai,Heping Wang +1 more
TL;DR: In this paper, the sharp asymptotic order of the quantity γ = n→∞ for a unit ball with an A∞ weight w on the domain Ω, which denotes either the unit sphere or the unit ball, or the standard simplex of the Euclidean space ℝd, was established.
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Full length article: Relating smoothness to expressions involving Fourier coefficients or to a Fourier transform
TL;DR: Coefficients of expansion of a function by trigonometric, algebraic and spherical harmonic orthogonal polynomials are related to the smoothness of that function.
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