Polynomial Approximation and $\omega^r_\phi (f,t)$ Twenty Years Later

zbMath1181.41002arXiv0709.2729MaRDI QIDQ3406471

Z. Ditzian

Publication date: 16 February 2010

Full work available at URL: https://arxiv.org/abs/0709.2729

zbMATH Keywords

polynomial approximationmoduli of smoothness\(K\)-functionalsBernsteinrealization functionalsJacksondirect and converse inequalitiesMarchaudNikol'skii and Ul'yanov type inequalities

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Fractional derivatives and integrals (26A33) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Best approximation, Chebyshev systems (41A50) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Continuity and differentiation questions (26B05) Convexity of real functions in one variable, generalizations (26A51) Approximation by positive operators (41A36) Approximation by other special function classes (41A30) Inverse theorems in approximation theory (41A27) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Research exposition (monographs, survey articles) pertaining to approximations and expansions (41-02) Saturation in approximation theory (41A40)

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Polynomial approximation with doubling weights ⋮ Unnamed Item ⋮ Differential calculus for linear operators represented by finite signed measures and applications ⋮ Multivariate approximation theorems in weighted Lorentz spaces ⋮ Strong estimates of the weighted simultaneous approximation by the Bernstein and Kantorovich operators and their iterated Boolean sums ⋮ A generalized modulus of smoothness ⋮ Approximation by the Bernstein-Durrmeyer operator on a simplex ⋮ Polynomial approximation in Sobolev spaces on the unit sphere and the unit ball ⋮ Estimates of the coefficients of the Jacobi expansion by measures of smoothness ⋮ Asymptotic constant in approximation of twice differentiable functions by a class of positive linear operators ⋮ New moduli of smoothness: weighted DT moduli revisited and applied ⋮ Polynomial approximation with doubling weights having finitely many zeros and singularities ⋮ Yet another look at positive linear operators, \(q\)-monotonicity and applications ⋮ Strong converse inequality for linear combinations of Szász-Mirakjan operators ⋮ Jacobi weights, fractional integration, and sharp Ulyanov inequalities

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