Multivariate Jackson inequality

DOI10.1016/j.cam.2009.02.095zbMath1181.41018OpenAlexW2169262015MaRDI QIDQ1035637

Wiesław Pleśniak

Publication date: 4 November 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.02.095

zbMATH Keywords

Markov inequalityJackson theoremSiciak extremal functionWhitney regularityapproximation and extension of infinitely differentiable functions

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Rate of convergence, degree of approximation (41A25) Inequalities for trigonometric functions and polynomials (26D05) Plurisubharmonic extremal functions, pluricomplex Green functions (32U35)

Related Items (12)

Jackson's inequality in the complex plane and the Łojasiewicz-Siciak inequality of Green's function ⋮ Polynomial fitting and interpolation on circular sections ⋮ Compression of Multivariate Discrete Measures and Applications ⋮ Geometry of holomorphic mappings and Hölder continuity of the pluricomplex Green function ⋮ The Newton product of polynomial projectors. II: Approximation properties ⋮ Algebraic cubature by linear blending of elliptical arcs ⋮ Numerical hyperinterpolation over nonstandard planar regions ⋮ A new constructive and elementary proof of a Bernstein-Walsh theorem, improved to infinite order convergence, for functions \(C^\infty\) in an intricate but smooth two-dimensional real domain ⋮ Łojasiewicz-type inequalities in complex analysis ⋮ Small perturbations of polynomial meshes ⋮ Polynomial Chaos Expansions for the Stability Analysis of Uncertain Delay Differential Equations ⋮ On the Use of Compressed Polyhedral Quadrature Formulas in Embedded Interface Methods

Cites Work

• Markov's inequality and the existence of an extension operator for \(C^{\infty}\) functions
• Markov's inequality and \(C^{\infty}\) functions on sets with polynomial cusps
• Differentiable functions
• On Some Extremal Functions and their Applications in the Theory of Analytic Functions of Several Complex Variables
• Extremal plurisubharmonic functions in $C^N$
• Approximation of Analytic Functions on Compact Sets and Bernstein's Inequality
• Siciak's extremal function in complex and real analysis
• Remez-Type Inequalities on the Size of Generalized Polynomials
• On superposition of quasianalytic functions
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