Bernstein-Walsh type theorems for real analytic functions in several variables

DOI10.1007/s00365-010-9097-4zbMath1230.41002OpenAlexW2008983734MaRDI QIDQ628673

Christiane Kraus

Publication date: 14 March 2011

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

Full work available at URL: https://doi.org/10.1007/s00365-010-9097-4

zbMATH Keywords

pluricomplex Green functionreal analytic functionsSiciak extremal functionBernstein-Walsh type theorems in higher dimensionsmaximal convergence

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Removable singularities in several complex variables (32D20) Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs (32E30) Plurisubharmonic functions and generalizations (32U05) Plurisubharmonic extremal functions, pluricomplex Green functions (32U35)

Related Items (1)

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

Cites Work

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• Multivariate polynomial approximation of powers of the Euclidean distance function
• The extremal psh for the complement of convex, symmetric subsets of \({\mathbb{R}}^ N\)
• Bernstein theorems for elliptic equations
• On the convergence of multivariable Lagrange interpolants
• Maximal convergence theorems for functions of squared modulus holomorphic type in \(\mathbb R^2\) and some applications
• The Complex Equilibrium Measure of a Symmetric Convex Set in R n
• Siciak's extremal function of convex sets in $C^N$
• On Some Extremal Functions and their Applications in the Theory of Analytic Functions of Several Complex Variables
• Extremal plurisubharmonic functions in $C^N$
• Uniform Harmonic Approximation on Compact Sets in $\mathbb{R}^k $, $k \geqq 3$
• Approximation of Analytic Functions on Compact Sets and Bernstein's Inequality
• On the Convergence and Overconvergence of Sequences of Polynomials of Best Simultaneous Approximation to Several Functions Analytic in Distinct Regions
• Note on the approximation of powers of the distance in two-dimensional domains

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