New moduli of smoothness on the unit ball and other domains, introduction and main properties

DOI10.1007/s00365-014-9232-8zbMath1314.26004OpenAlexW2079147741MaRDI QIDQ485325

Z. Ditzian

Publication date: 9 January 2015

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-014-9232-8

zbMATH Keywords

best approximationmoduli of smoothnessorthogonal expansion\(K\)-functionalsholomorphic semigroupsfunction spaces on the unit ballrealization functionalssphere and simplex

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Groups and semigroups of linear operators (47D03) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Approximation by polynomials (41A10) Approximation by positive operators (41A36) Inverse theorems in approximation theory (41A27) Special properties of functions of several variables, Hölder conditions, etc. (26B35)

Related Items (4)

Problems and conjectures in approximation that I would like settled ⋮ New moduli of smoothness on the unit ball, applications and computability ⋮ On the K-functional in learning theory ⋮ Best polynomial approximation in \(L_w^2 ( S )\) for the simplex \(S\)

Cites Work

• Smoothness and best approximation with respect to Freud-type weights, a new approach
• Rearrangement invariance and relations among measures of smoothness
• Classical diffusion processes and total positivity
• Cesàro summability and Marchaud inequality
• Jackson inequality for Banach spaces on the sphere
• Moduli of smoothness and approximation on the unit sphere and the unit ball
• Approximation by spherical functions
• Fractional derivatives and best approximations
• Some equivalence theorems with \(K\)-functionals
• Convexity, moduli of smoothness and a Jackson-type inequality
• Approximation on Banach spaces of functions on the sphere
• Equivalence of measures of smoothness in L_p(S^d-1), 1<p<∞
• Strong converse inequality for Poisson sums
• A SURVEY OF POLYNOMIAL APPROXIMATION ON THE SPHERE
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• Strong converse inequalities
• A modulus of smoothness on the unit sphere
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: New moduli of smoothness on the unit ball and other domains, introduction and main properties