Distribution of interpolation points
type: Item
instance of: scholarly article
title: Distribution of interpolation points
zbMATH Open document ID: 0862.30037
DOI: 10.1007/BF02559510
author: R. Grothmann
published in: Arkiv för Matematik
publication date: 1997-05-25T00:00:00Z
review text: Let \(E\) be a compact subset of the complex plane with regular boundary \(\partial E\) and with connected complement. Let \(f: E\to\mathbb{C}\) be a continuous function such that there exists a sequence of polynomials of degree at most \(n\) with \(\varlimsup_{n\to\infty}|f-P_n|^{1/n}_E={1\over r}\) for \(r>1\) and such that \(f-P_n\) has \(n+1\) zeros on \(\partial E\). The author proves that the sequence of counting measures associated to these points contains a subsequence which converges to the equilibrium measure on \(E\) in the weak sense. Conversely, the analyticity of a function \(f\) on an open set containing \(E\) is proved, provided that the sequence of measures mentioned above converges to a unit measure \(\sigma\) and additionally the interpolation polynomials tend to \(f\) geometrically.
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 896435
zbMATH Keywords: interpolation
zbMATH Keywords: approximation in the complex domain
reviewed by: Klaus Menke
MaRDI profile type: Publication
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cites work: On the real CF-method for polynomial approximation and strong unicity constants
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description: scientific article; zbMATH DE number 896435