On the convergence of multivariable Lagrange interpolants
type: Item
instance of: scholarly article
title: On the convergence of multivariable Lagrange interpolants
zbMATH Open document ID: 0683.32011
DOI: 10.1007/BF01889619
author: Thomas Bloom
published in: Constructive Approximation
publication date: 1989-01-01T00:00:00Z
review text: The author considers a triangular array of nodes in the compact set \(X\subseteq {\mathbb{C}}^ n\) and, for the analytic function f in a neighborhood of X, the corresponding Lagrange interpolant \(L_ d(f)\) of degree d at the given nodes. The main object of the paper is to obtain conditions of uniformly convergence of the sequence \(\{L_ d\}_{d\geq 1}\) to f on X. For example, if X is locally regular the author constructs a function \(\phi\) satisfying the Monge-Ampère equation on \({\mathbb{C}}^ n\setminus X\) such that if f is analytic on \(\{\) \(\phi\leq R\}\), \(R>1\), then \[ \| L_ d(f)-f\|_ X\leq B \exp (-d\cdot \log R), \] with convenable B. Numerous examples and relations between results are also presented.
Mathematics Subject Classification ID: 32E30
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 4118706
zbMATH Keywords: multivariable Lagrange interpolation
zbMATH Keywords: extremal plurisubharmonic function
zbMATH Keywords: complex Monge-Ampère equation
reviewed by: Ioan Şerb
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4118706