Bernstein-Chebyshev inequality and Baran's radial extremal function on algebraic sets

DOI10.14658/PUPJ-DRNA-2021-3-3MaRDI QIDQ6558234

Agnieszka Kowalska, Leokadia Białas-Cież

Publication date: 19 June 2024

Published in: Dolomites Research Notes on Approximation (Search for Journal in Brave)

zbMATH Keywords

Green's functionBernstein inequalityalgebraic setsBaran's radial extremal functionPleśniak type property

Mathematics Subject Classification ID

Computational aspects of higher-dimensional varieties (14Q15) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Computational aspects of algebraic curves (14Q05) Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs (32E30)

Cites Work

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• Invariance of polynomial inequalities under polynomial maps
• Hölder continuity of the Green function and Markov brothers' inequality
• Markov's inequality and the existence of an extension operator for \(C^{\infty}\) functions
• Polynomial inequalities on certain algebraic hypersurfaces
• Extremal growth of polynomials
• Characterization of compact subsets of algebraic varieties in terms of Bernstein type inequalities
• Extremal plurisubharmonic functions in $C^N$
• Sets with the Bernstein and generalized Markov properties
• On the behaviour of constants in some polynomial inequalities
• Markov and Division Inequalities on Algebraic Sets

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